Method of and apparatus for nuclear quadrupole resonance testing a sample

ABSTRACT

A method of nuclear quadrupole resonance testing a sample is disclosed in which the excitation applied to the sample is arranged so that phase and amplitude information may be obtained from the response signal, and in which the signal is resolved into two components. Particularly if a parameter such as radio-frequency field strength varies with position, this may give an indication of the distribution of nuclei in the sample, preferably from the phase of the response signal. Positional information can also be obtained by measuring from two or more reference points. This may be employed in imaging. The phase information may be employed to improve the signal to noise ratio obtainable in other methods where only amplitude information was previously available, for example in distinguishing genuine NQR response signals from spurious signals.

The present invention relates to a method of and apparatus for nuclearquadrupole resonance testing a sample, and is applicable in one aspectto imaging a sample based on its nuclear quadrupole resonance (NQR)response. The invention has particular application to the detection ofthe presence of a given substance in a sample, and more particularly tothe determination of the position and/or amount of material.

Nuclear Magnetic Resonance (NMR) techniques are now widely used forimaging, particularly medical imaging, e.g. using proton resonance.However, NMR investigations require a strong and highly homogeneousstatic magnetic field to operate, and this requires bulky and expensiveequipment. In addition, due to the strong magnetic field, the methodcannot be used in the presence of ferrous objects.

Nuclear quadrupole resonance (NQR) responses can be detected withoutrequiring the presence of a strong static magnetic field, and sointerest in using the NQR response of a body to probe its structure hasrecently developed. However, because NQR is a different phenomenon toNMR, existing NMR techniques cannot be directly applied to NQRinvestigations.

NQR testing has been increasingly widely used for detecting the presenceor disposition of specific substances. The phenomenon depends ontransitions between energy levels of quadrupolar nuclei, which have aspin quantum number I greater than or equal to 1, of which ¹⁴N is anexample (I=1). ¹⁴N nuclei are present in a wide range of substances,including animal tissue, bone, food stuffs, explosives and drugs. Thebasic techniques of NQR testing are well-known and are discussed innumerous references and journals, so will only be mentioned brieflyherein.

In conventional Nuclear Quadrupole Resonance testing a sample is placedwithin or near to a radio-frequency (r.f.) coil and is irradiated withpulses or sequences of pulses of electro-magnetic radiation having afrequency which is at or very close to a resonance frequency of thequadrupolar nuclei in a substance which is to be detected. If thesubstance is present, the irradiant energy will generate an oscillatingmagnetization which can induce voltage signals in a coil surrounding thesample at the resonance frequency or frequencies and which can hence bedetected as a free induction decay (f.i.d.) during a decay period aftereach pulse or as an echo after two or more pulses. These signals decayat a rate which depends on the time constants T₂* for the f.i.d., T₂ andT_(2e) for the echo amplitude as a function of pulse separation, and T₁for the recovery of the original signal after the conclusion of thepulse or pulse sequence.

The present invention, in one aspect, is particularly concerned withprobing a sample to obtain information dependent on the position ordistribution of resonant nuclei within a sample. This may be used toproduce an image of the sample.

It is known that the NQR response of nuclei in a crystal is dependent onthe environment of the nuclei, and also on factors such as the strengthof the exciting field. If the exciting radio-frequency (r.f.) fieldstrength varies throughout the sample, then the resonance response willalso be dependent on position within the sample, and this can inprinciple be used to give an indication of the position of resonantnuclei within a sample.

A method for obtaining positional information using NQR, employing anr.f. field gradient, and not requiring a static magnetic field, has beenproposed by Rommel, Kimmich et al. (Journal of Magnetic Resonance 91,630-636 (1991) and also U.S. Pat. No. 5,229,722). Those disclosures (seepage 631, line 25 of the paper and column 6, lines 46-50 of the patent)teach that NMR techniques such as phase-encoding (in which both thephase and the amplitude of the r.f. signal received from the sample areused to obtain information about the sample) cannot be applied to NQRimaging, and that only amplitude encoding is possible with NQR imaging.In other words, it is stated that it is only possible to extract asingle parameter (signal amplitude) from an NQR imaging experiment whichuses an r.f. field gradient in the absence of a static magnetic field.This is stated to be consistent with the theory that the transversemagnetisation associated with an NQR response oscillates, in contrast tothe precession about the applied magnetic field observed in an NMRexperiment.

Our earlier United Kingdom Patent Number GB-2,257,525 discloses a methodof imaging using NQR in which a field gradient is imposed upon a sample.Reference should be made to that disclosure for useful backgroundinformation and further discussion of the art of imaging using NQR whichis not repeated here. In that patent, surprisingly advantageous resultswere obtained by subjecting a sample to a field having a particularpositional dependence. Although that method can enable a satisfactoryimage to be obtained, there is still some room for improvement.

The present invention seeks to provide a method and apparatus forprobing a sample by detecting its NQR response which alleviates some orall of the drawbacks of previous methods. Preferred arrangementsdisclose a probing technique in which positional information may beobtained even in the absence of a controlled static magnetic field.

The invention is applicable to detection of quadrupolar nuclei (I≧1) andis particularly applicable to nuclei such as ¹⁴N (I=1) in whichadvantageous results can readily be obtained in the absence of a staticmagnetic field, but may be used for detecting other quadrupolar nuclei,for example I=3/2, I=5/2 etc. The invention is particularly applicableto polycrystalline samples, or samples containing one or morepolycrystalline clusters of quadrupolar nuclei.

In developing the invention, it has been appreciated that there are manyNQR applications in addition to imaging in which it would be desirableto obtain more information than signal amplitude, but this has hithertonot been possible from a single measurement.

Surprisingly, the inventors have found that two independently varyingcomponents (e.g. phase and amplitude dependent components) can beextracted from a received NQR response signal if the excitation isselected appropriately. A preferred method of achieving this is to usetwo excitation pulses of selected phase. This can lead to a morereliable classification of the object under test.

The prior art has not reported detection of two independently resolvablecomponents resulting from NQR interactions. Indeed, theory predicts onlya single component is to be found, and Rommel et al. states that phaseencoding is not possible in NQR experiments.

The phase and amplitude dependent components may actually be phase andamplitude, but it is to be understood that references herein to phaseand amplitude dependent components are intended to include componentsderived from or related to the phase and amplitude of the responsesignal without necessarily being directly representative thereof. Inparticular, the signal may be resolved into two components, both ofwhich vary as functions of both phase and amplitude. For example, in apreferred arrangement, the received signal is (initially) resolved intotwo components having a quadrature relationship. Phase-relatedinformation may be obtained by combining the two components in a firstmanner (e.g. comprising determining a ratio of the components) andamplitude-related information may be obtained by combining thecomponents in a second manner (e.g. comprising summing a function of thecomponents).

The extra information obtainable by the provision of both phase andamplitude information in an NQR experiment may be useful in a number ofways, as will be understood by one skilled in the art based on thediscussion below.

In an imaging experiment, the provision of both phase and amplitudeinformation can provide better classification of the sample than theamplitude encoding alone technique of Rommel et al. where the receivedsignal amplitude is dependent on both the position (as intended in theexperiment) and also on the amount of resonant material present. Thiscan alleviate one problem of Rommel's technique that unless the amountof resonant material is known, it may not be possible to determine itsposition accurately, and vice versa.

The phase and amplitude information may be used together to improvesignal to noise ratio in any of a number of experiments where onlyamplitude information was previously available.

Thus, based on the results of the above surprising finding, theinvention provides, in one aspect, a method for nuclear quadrupoleresonance testing a sample containing quadrupolar nuclei, comprisingapplying excitation to the sample, the excitation being selected toproduce a response signal containing detectable phase and amplitudecomponents resulting from nuclear quadrupole resonance interactionbetween said excitation and said quadrupolar nuclei, detecting theresponse signal, resolving the response signal into (independentlyvariable) phase and amplitude dependent components and processing theresponse signal on the basis of both components.

In this specification, references to processing the response signal onthe basis of both components are preferably intended to imply processingthe response signal as if it were a function of two independentvariables (phase and amplitude), and in particular may include resolvingthe response signal into two independent quantities (e.g. phase andamplitude). This is to be contrasted with processing (for example inwhich a phase sensitive detector may be employed to detect signals of aparticular phase) in which phase information is not measured as anindependently varying quantity.

Preferably a plurality of values of the response signal are sampled(preferably for different excitation conditions e.g. pulse lengths) anda plurality of values of a phase parameter (e.g. phase or the ratio ofreal and imaginary components) varying as a function of the phase of theresponse signal substantially independently of the response signalamplitude are determined. Determination of variation of a phaseparameter (preferably in addition to determination of an amplitudeparameter) for several values of the response signal may enable usefulinformation, e.g. positional information or information useful in noisereduction to be gained from the response signal.

According to a preferred arrangement, the excitation comprises first andsecond pulses differing in phase by a predetermined angle. This canprovide a convenient method of exciting the desired response in apredictable manner.

The angle is preferably about 90° as this may enable two substantiallyindependent components to be resolved.

The two pulses are preferably transmitted from the same coil (or coils);this may provide convenience and ease of establishing phase correlationbetween the pulses.

The pulses may be separated by a time period, which is preferablyrelatively short, e.g. substantially shorter than the f.i.d.(Free-induction decay) time, T₂*, and preferably zero or as close tozero as possible; that is, the pulses are preferably contiguous. Acomposite pulse is preferred, the first and second pulses beingsubstantially contiguous but differing in phase; this may shortenoverall measurement times, and may improve response signal amplitudes.

In a preferred arrangement, the excitation comprises two pulses ofsubstantially equal duration, but different phase. Use of pulses ofequal duration may simplify calculation of position (where position isdetermined) of the responsive material or other processing of the data.However, if the durations differ, and preferably if the response signalis determined for a plurality of different relative durations, this maybe useful in obtaining a more precise determination of the position of aresponsive substance in a sample.

The pulses are preferably of substantially equal amplitude; thissimplifies the equipment needed and may simplify processing of the data.

It is particularly advantageous if the second pulse is arranged (atleast partially) to lock the magnetisation (of the quadrupolar nuclei)generated by the first pulse. Such a sequence may be termed a “spinlocking” sequence, with the magnetization being locked for a time longerthan would be achievable with the equivalent single pulse. Locking canbe achieved by keeping the B₁ field of the second pulse parallel to themagnetization produced by the first pulse. This may enable a strongerand longer lasting signal attributable to the first pulse to bedetected.

Preferably also, the excitation includes a third pulse selected to lock(at least partially) the net magnetization produced by the first twopulses, and preferably being of phase intermediate that of the first andsecond pulses. This can further assist in locking the magnetization, andmay result in a higher signal to noise ratio or better interferencesuppression. It may also be useful in selecting components of aparticular phase, and this may be useful in selecting signals emanatingfrom a particular region of the sample. This may also be provided as afurther independent aspect, in a method of detecting NQR responsesignals emanating from quadrupolar nuclei in a given region of a sample,the method comprising exciting the sample to produce a response signalfrom the quadrupolar nuclei having a phase varying as a function of theposition of the nuclei and identifying signals of a given phase, whereinsaid identifying preferably comprises applying a pulse arranged to lockresponse signals of said given phase.

Although reference is made above to a single series of two or threepulses, it will be understood that several series of excitation pulsesmay be used, and signals detected after excitation with some or all ofsaid series. For example, a series of pulses may be used to lock spins.This may be useful in reducing interference or spurious signals due toother objects (e.g. metallic objects, particularly nickel platedobjects) within a sample.

It will be understood that references in the present specification tophases differing or being equal is equivalent in certain circumstancesto references to frequency differing or being equal, in that a change inphase implies an at least momentary change in frequency and vice versa.

In one practical arrangement, a phase-sensitive detector may be employedto detect the phase and amplitude dependent components as two componentshaving a pre-determined phase relationship, most preferably a quadraturephase relationship. This may provide a convenient way of detecting twocomponents in the signal. With this arrangement, the first and secondcomponents may correspond to the components along the x and y axis ofthe rotating frame, and in what follows these will be referred to as thereal and imaginary components of the received signal.

Preferably a parameter varying as a function of phase is obtained from aratio of the two components. This may enable simple but effectivedetermination of a phase parameter.

Most preferably, at least the field strength of the excitation variesthroughout at least a portion of the sample according to a givenpattern. This is similar to the case with surface coils, well-known inmagnetic resonance imaging, and provides a readily implementable way ofproviding a response signal which encodes or conveys informationconcerning the distribution or position of responsive nuclei in thesample to be obtained. In a preferred arrangement for achieving this,the excitation pulses are transmitted to the sample from a coil whichproduces a non-uniform r.f. field in the vicinity of the sample. Ther.f. field amplitude preferably varies with position in a known manner.

In a preferred arrangement, the field strength and duration are selectedto produce a variation of flip angles within a range of 0 to 2π (360degrees) throughout a region of interest of the sample, and preferablythroughout the sample. The minimum usable flip angle will depend onnoise and other considerations, but in some cases may be of the order ofa few degrees. Preferably the maximum flip angle in the sample (or atleast the region of interest) does not exceed 2π. Keeping all flipangles below 2π may allow the measured phase to be a single-valuedfunction of position, which may simplify determination of position.

It will be appreciated by those skilled in the art that the flip anglefor a given pulse duration and amplitude is dependent on I, the nuclearspin quantum number as well as on the gyromagnetic ratio; the spinquantum number I affects the order of the Bessel function which governsthe variation of effective flip angle with pulse duration and amplitude.In this specification, a flip angle of 2π is intended to refer to areturn of the magnetisation vector M into parallellism with its originalorientation (which equates to a particular product of pulse amplitudeand duration), and other flip angles are to be construed accordingly inproportion.

Preferably, position information representative of the position of saidnuclei is obtained based on at least the phase of the response signal.Using phase (rather than amplitude alone) to determine position mayenable positional determination to be substantially independent of theamount of responsive nuclei present. This may facilitate accuratedetermination with fewer measurements, for example in some cases asingle measurement may suffice.

Preferably, quantity information representative of the amount of saidnuclei is obtained based on at least the amplitude of the responsesignal, or based on the combined amplitude of two (preferablyorthogonal) components into which the signal is resolved. This can beused in adjusting the results to take into account the amount ofresponsive nuclei, and, if combined with positional information, canallow a distribution of nuclei in the sample to be calculated.

Preferably, the received components are analysed to obtain profileinformation representative of the distribution of said nuclei in saidsample. This may be useful in locating NQR responsive substances withina body, and may be developed to provide an image of the interior of thebody.

The received components may be analysed to obtain profile informationrepresentative of variation of an environmental parameter, preferablytemperature or pressure, which affects said NQR response in said sample.This may be useful in thermal or stress analysis.

Whilst both depth and position information can be obtained from theresponse to a single excitation (a composite pulse or pair of pulses)for a simple sample as discussed above, in an advantageous development,the excitation is applied repeatedly to the sample, and the analysis isrepeated (preferably with at least one factor affecting the responsevarying as the excitation is repeated) to obtain a plurality of sets ofsaid profile information. This may enable more accurate analysis of thesample, and preferably at least one further set of profile informationof higher resolution and/or higher signal-to-noise ratio is obtainedfrom said plurality of sets.

The factor is preferably at least one of excitation pulse duration andexcitation field strength. This may provide an easily implementablemethod of optimising the excitation or obtaining multiple measurements.

For example, one or more of the pulse length and B₁ field may be variedin a number of steps over the range of flip angles selected, in whichcase the resolution will be determined by the number of steps in eachexperiment, the greater the number of steps, the greater the resolution.

The duration of the pulses may be varied, for example in a series ofincrements. This may be used to extend the measurable depth over whichnuclei can be detected or to improve the resolution at whichdetermination can be made or to resolve ambiguities resulting fromanalysis of data from a single measurement or to improve the signal tonoise ratio.

The relative durations of the first and second pulses may be varied, andpreferably the total duration of the two pulses is kept substantiallyconstant. For example, a series of measurements may be made, rangingfrom a relatively short first pulse and long second pulse throughsubstantially equal durations to a relatively long first pulse and shortsecond pulse. This may be useful in distinguishing signals from aparticular location more accurately.

The amplitude (field strength) of the exciting pulse may be varied. Thisis preferably in a series of discrete increments, but may besubstantially continuous or quasi-continuous in certain cases. This mayenable accurate resolution of position, or may enable uncertainties ordegeneracies in the distribution to be resolved, and may be particularlyuseful in reducing noise which may be present when the sample is distantfrom the transmitter coil(s).

The method may include obtaining a plurality of sets of profileinformation, corresponding to profiles at different positions or indifferent directions. This may be used in further characterisation ofthe sample, or determination of crystal orientation, and may be usefulin imaging.

The excitation may be applied from two or more directions, preferablysubstantially orthogonal, and said profile information obtained for eachdirection. For example, the sample may be probed from different (e.g. 3orthogonal) directions; this may be useful in obtaining a composite3-dimensional image.

The sample may be physically moved with respect to the coil (i.e. bymoving either or both of the sample and the coil). This is simple toimplement, and has the advantage that a direct correlation betweenphysical position and observed readings can readily be obtained. It maybe useful, particularly in combination with other methods discussedbelow, for scanning in one direction for example to assemble a 3D imagefrom a series of 2D slices, where an article is already moving. It maybe useful, for instance, for imaging packages on a conveyor belt.

Thus, the profile information may be used for forming an image of thesample, the method further comprising constructing an image of thesample from at least one set of profile information.

In addition to imaging of the distribution of material in an object, theinvention may also be applied to characterisation of temperatureprofiles within a sample. Alternatively, the method may be used forcharacterisation of other parameters which affect the resonance responseof a sample, for example pressure—this may be used for example toproduce a stress profile of a sample. Other applications will beapparent to those skilled in the art.

Thus, in an important second aspect, the invention provides a method offorming an image of a sample containing quadrupolar nuclei, the methodcomprising applying excitation to the sample, the excitation having afield strength preferably varying according to a given function ofposition and being selected to produce a detectable response signalresulting from NQR interaction between the excitation and thequadrupolar nuclei, the response signal being resolvable intophase-dependent and amplitude-dependent components, resolving theresponse signal into two received components representative of saidphase-dependent and amplitude-dependent components and, based on bothreceived components, producing an image representative of thedistribution and/or environment of said nuclei in the sample.

Preferably the excitation is repeated a plurality of times (preferablyat least 10, 20, 50, 100, 200, 500, 1000 or more times) and at least oneof excitation pulse amplitude and excitation pulse duration is varied asthe excitation is repeated. This may yield a set of received componentswhich may be processed to produce an image. The step of producing animage may include transforming the data (from a plurality ofrepetitions), for example according to a Hankel transform or a Fouriertransform, or may include correlating the data to a distribution patternwhich would be expected to produce similar data, for example by aMaximum Entropy Method.

Preferably the position of responsive nuclei is determined based on aphase parameter which varies as a function of phase of the receivedcomponents and is determined either from the phase of the receivedsignal or from a combination of two received components which vary withboth phase and amplitude of the received signal, for example from aratio of two quadrature components.

A visual output may be produced of the image.

The second aspect may use any of the preferred or optional features ofthe previous aspect, and may include the previous aspect.

In addition to the imaging and profiling facilitated by use of phase, asbriefly mentioned above, the phase information provided by the method ofthe first aspect may be used to suppress noise (this may still beapplied where the phase information is additionally used in imaging).Thus, a preferred method includes obtaining a phase parameter (whichvaries as a function of phase of the detected signal) from the resolvedcomponents, and processing both resolved components using the phaseparameter to produce an output having a signal-to-noise ratio greaterthan that of the response signal amplitude.

This important feature may be provided as a third aspect in a method ofprobing a sample to detect quadrupolar nuclei therein, the methodcomprising applying excitation to the sample, the excitation beingselected to stimulate a response signal having detectable phase andamplitude components resulting from NQR interactions with thequadrupolar nuclei, detecting the response signal and resolving thedetected signal into phase-dependent and amplitude-dependent components,obtaining a phase parameter from the resolved components and processingboth resolved components using the phase parameter to produce an outputhaving a signal-to-noise ratio greater than that of the response signalamplitude.

Preferably, the processing includes identifying mutually inconsistentvalues of the resolved components as representative of spurious signals.This may provide an efficient way of filtering out spurious signals. Thephase parameter obtained with the invention is unique to NQR responsesignals, as it depends on the polycrystalline nature of the sample andthe known dependence of the transition probability on the orientation ofB₁ in the electric field gradient frame of reference; piezo-electricresponses or acoustic ringing will not exhibit the same phaserelationships.

The processing may include applying a first excitation to produce afirst received signal in which a desired signal has a first phasedependence, and applying a second excitation to produce a secondreceived signal in which the desired signal has a second phasedependence, and detecting the desired signal on the basis of the firstand second received signals and corresponding measured phase dependencethereof. Thus, the desired signals may be found by looking for aparticular phase “signature”.

Preferably also, the true quadrupole resonance signal is distinguishedfrom any spurious signal in dependence on its (time) gradient, curvatureor shape, perhaps in dependence upon whether the true and spurioussignals have gradients of opposite sign.

The preferable and optional features discussed above in relation toother aspects may apply to this aspect, as will be well-understood byone skilled in the art.

The excitation may be varied to enable reliable imaging for a variety ofenvironmental parameters (e.g. temperature), as discussed in our earlierpatent application published as GB-A-2,284,898.

The above aspects may provide reliable methods for obtaining positionalinformation.

The accuracy of the positional information obtained may be enhanced bydetermining the distances of a cluster of responsive (quadrupolar)nuclei from two or more reference points and calculating positionalinformation based on the respective distances.

This can be provided independently, and according to a fourth aspect,the invention provides a method of determining the position ofquadrupolar nuclei in a sample comprising applying excitation to thesample to produce a detectable NQR response, detecting a first responsesignal from said nuclei and determining a first distance of the nucleifrom a first reference point; detecting a second response signal todetermine at least a second distance of the nuclei from at least asecond reference point; and determining positional information of saidnuclei on the basis of said distances from said reference points. Thefirst and second response signals may be detected by separate receivercoils at positions corresponding to the reference points.

The positional information may actually be the position of the nuclei ina particular reference frame, but the term “positional information” isintended to include any position-related parameter; for example velocityor acceleration may be determined by such a method.

Preferably, the positional information is determined by triangulation,and in a preferred arrangement a third distance from a third referencepoint is determined.

A plurality of coils may be used for transmission and/or reception ofsignals, each coil preferably being associated with a correspondingreference point; preferably a plurality of receiver coils are used todetect the response signal produced after excitation from a transmittercoil arrangement.

The detection of the distances from each reference point may besequential or simultaneous.

The fourth aspect may be used independently, but preferably is combinedwith one of the earlier aspects; this can provide a more accurateindication of position. Most preferably, the excitation is arranged sothat the phase of the response signal varies with the position ofresponsive (quadrupolar) nuclei with respect to a transmitter coil, andpreferably both the phase and amplitude of the detected signal from eachof a plurality of receiver coils is used to determine positionalinformation.

The above methods may be applied to detection of a single substance at asingle resonance frequency. It is also possible, and may be highlydesirable in certain applications to repeat the measurements for avariety of different frequencies, corresponding to resonant frequenciesof various substances of interest. For example, a sample may be scannedat frequencies corresponding to the resonant frequencies of one or moreknown explosives or components of explosives and/or at frequenciescorresponding to one or more known narcotics or narcotic components.

Alternatively, the frequencies may correspond to resonant frequencies ofbiological substances of interest in a patient. The results of each scanmay be combined to produce a better characterisation of the sample undertest, for example by overlaying images obtained from each scan. This mayproduce a composite image (which may be displayed as a colour-codedimage) identifying particular regions of interest within an article. Inaddition the results of one or more such scans may be combined with orcompared to characterisation, such as images, obtained by other methods,for example X-Ray imaging.

In addition to the substances discussed above, the above NQR testing orimaging aspects of the invention may be applied to detection ofproteins, hormones and other constituents of a human or animal body, forinstance for medical imaging. Of particular interest in this respect isdetection of ¹²⁷I (I=5/2), which is present in thyroxin.

Surprisingly, it has been found that although nitrogen is readilydetectable in compounds such as explosives using NQR testing, and ispresent in most biological compounds including proteins, detecting theNQR response of iodine in a biological compound or complex containingiodine (and nitrogen) may give advantageous results.

Based on this surprising finding, in a fifth aspect, the inventionprovides a method for NQR testing a biological specimen containing aparticular substance containing iodine nuclei and preferably otherquadrupolar nuclei (most preferably nitrogen), comprising applyingexcitation to the specimen, the excitation being arranged to produce anNQR response from the iodine nuclei, and detecting the response signalfrom said iodine nuclei (if present). Although detection of nitrogen insubstances such as explosives has been found to work well, it hashitherto been troublesome to detect biological substances such asproteins from their NQR response.

This may be used in conjunction with the other aspects and preferredfeatures described herein, and may in particular be used in conjunctionwith the imaging methods described.

Particularly useful results are obtained if the substance is thyroxin ora thyroxin derivative, precursor or analogue, and preferably wherein thespecimen includes a mammalian thyroid gland. As well as ¹²⁷I, otherquadrupolar nuclei such as ³⁵Cl (I=3/2) may be detected in a similarway. This may be particularly useful in “tagging” experiments where itis required to follow the rate of uptake or loss of a given taggedspecies, for example in the thyroid gland or other organs such as thekidneys or liver.

The invention also provides apparatus arranged to perform all methodsdisclosed herein.

In a sixth aspect, the invention provides apparatus for detecting an NQRresponse in a sample containing quadrupolar nuclei, the apparatuscomprising excitation means arranged to generate an excitation signalcapable of exciting an NQR response having detectable phase andamplitude components; transmission means arranged to transmit theexcitation signal to the sample; detection means arranged to detect aresponse signal generated by the sample to produce a detected signal;resolving means arranged to resolve the detected signal into first andsecond components; signal processing means connected to the resolvingmeans to receive both components for processing the response signalbased on both phase-dependent and amplitude-dependent componentsthereof; and control means for controlling operation of the apparatus.

The excitation means may be arranged to generate at least two pulsesdiffering in phase by a predetermined angle, preferably 90 degrees, orother advantageous excitation waveforms discussed above in relation tothe method aspects.

The transmission means may be arranged to generate a radio-frequencyfield having a field strength varying according to a given patternthroughout at least a portion of the sample; this may enable positionalinformation to be detected from the response signal. The control meansmay be arranged to cause the transmission means to generate a pluralityof said given patterns. This may enable several measurements to be madeunder different conditions.

The transmission means may comprise at least first and second coils (forexample of different sizes and/or at different positions ororientations) for producing respectively, on excitation with aradio-frequency electrical signal, at least first and secondradio-frequency fields varying in strength as different functions ofposition in the vicinity of the sample, wherein adjustment of therelative amplitudes of electrical signal supplied to each coil altersthe pattern of the net radio-frequency field. These may include a coil(e.g. a coil arrangement such as a Helmholtz pair) for generating afield having a substantially constant field strength in the vicinity ofthe sample. Such arrangements may facilitate application of a desiredfield pattern to a sample.

The apparatus preferably includes means to store or to calculate the oreach given pattern to provide an estimate of transmitted radio-frequencyfield strength at a plurality of positions, and having weighting meansfor determining an adjusted value of received signal strength based onthe received signal strength and the estimated field strength at aposition in the sample corresponding to the source of the receivedsignal. This may enable a more accurate determination of the amount ofresponsive nuclei in a sample from the received signal strength.

Preferably, the resolving means is arranged to resolve the receivedsignal into components having a quadrature relationship, for example byemploying a quadrature detector. This provides a convenient arrangementfor producing two components from which a phase parameter can bedetermined.

The apparatus may include means for causing a variation in at least oneenvironmental parameter which affects said NQR interaction throughout atleast a portion of the sample. This may be used for further encoding ofpositional information.

Preferably, the signal processing means is arranged to sample thedetected signal for a predetermined time, and to store two componentswhich together contain both phase and amplitude information. This mayfacilitate determination of a phase parameter.

Each feature of each method aspect of the invention can be applied tothe apparatus aspect as appropriate.

The phase information provided by the invention can be used in a numberof ways including those discussed in more detail below. In anotheraspect, the invention provides use of the phase of an NQR responsesignal from quadrupolar nuclei in the determination of the position ofthe nuclei, or in imaging of a sample containing the nuclei, or inreduction of noise in the NQR response signal.

Preferred features of the present invention are now described, by way ofexample only, with reference to the accompanying drawings, in which:

FIG. 1A is a schematic diagram of apparatus for NQR imaging according toa first embodiment of the present invention;

FIG. 1B is a schematic block diagram of apparatus for NQR testingaccording to a second embodiment of the invention.

FIG. 2 is a graph showing the NQR response to a single r.f. pulse;

FIG. 3 is a graph showing the real and imaginary NQR response to a pairof pulses of equal length differing in phase by 90 degrees;

FIG. 4 shows the data of FIG. 3 plotted as phase and magnitudeinformation;

FIG. 5 shows the data of FIG. 3 plotted over a range of flip angles of 0to 2π;

FIG. 6 shows the data of FIG. 4 plotted over a range of flip angles of 0to 2π;

FIG. 7 shows the ratio of expectation values of the real and imaginarycomponents of FIG. 5;

FIG. 8 is a plot of ratio of expectation values of real and imaginarycomponents against distance for an inverse cube field;

FIG. 9 is a plot of results obtained from a 200 g sample of RDX located6.9 cm from a 25 cm diameter spiral coil when excited at 5.1927 MHz;

FIG. 10 is a plot of results obtained from the same sample as in FIG. 9at a distance of 9.9 cm from the coil;

FIG. 11 is a plot of results obtained from the same sample as in FIG. 9at a distance of 14.9 cm from the coil;

FIG. 12 is a plot of the ratio of real and imaginary components from theresults of FIG. 9 (square boxes) and FIG. 11 (circles) respectively;

FIG. 13 is a plot of results obtained from a 32 g sample at a distanceof 5.2 cm and a 200 g sample at a distance of 14.9 cm from the 25 cmdiameter coil used to obtain the results of FIG. 9;

FIG. 14 is a plot of real and imaginary components and phase for twopulses of constant total flip angle, but differing lengths against theflip angle produced by the first pulse;

FIG. 15 is a plot showing variation of real and imaginary componentswith pulse length for off-resonance excitation with a single pulse, andvariation of amplitude with pulse length for on-resonance excitation;

FIG. 16 is a series of plots showing data obtained from a sample 6 cmwide at a distance of 7 cm from a coil compared to a series of predictedresults for different sample sizes and distances;

FIG. 17 is a plot of the probability of a sample being located at aparticular distance from a coil based on comparison of data obtainedfrom a sample 2.7 cm from a coil to a theoretical prediction; and

FIG. 18 is a plot of a profile obtained from three samples of RDX atdistances of 2, 7, and 16.5 cm from a coil respectively.

APPARATUS

Referring to FIGS. 1A and 1B, two embodiments of the apparatus will bedescribed first for a better understanding of the subsequent descriptionof the theoretical and method aspects of the embodiments of theinvention; the function of the various parts will become more clearduring the discussion of the techniques for testing and imaging.

EMBODIMENT 1

Referring to FIG. 1A, apparatus for NQR testing according to thisembodiment includes a radio-frequency source 11 connected via aphase/amplitude control 10 and a gate 12 to an r.f. power amplifier 13.The output of the latter is connected to an r.f. probe 14 containing oneor more coils by means of which the sample can be irradiated with r.f.pulses at the appropriate frequency or frequencies to excite nuclearquadrupole resonance in substances of interest. The arrangement of coilsin the probe 14 of this embodiment is discussed in more detail below.The frequency, phase, and power are controlled by control computer 16,as will be discussed below in the discussion of the method.

Coil Arrangement

In the first embodiment of the apparatus, the probe contains (inparallel) a spiral coil on one side of the sample and a Helmholtz pairlocated either side of the sample. One example of the spiral coil is anArchimedean spiral which produces a field which varies approximately asa function of r⁻³ (where r is distance from the coil); the Helmholtzpair produces a substantially constant field. An example of anotherarrangement which achieves a similar effect is a Helmholtz pair in whichone coil has more turns than the other. The amplitude of signals fed to(and received from) each coil is adjusted under the control of thecomputer 16 by means of switchable attenuator 26, which in thisembodiment is arranged to switch the amplitude of signals to each coilin discrete steps to allow several different field patterns to beestablished. In a modification of this embodiment, the amplitude ofsignals to each coil is continuously adjustable.

The same probe 14 functions as both a transmitter and receiver in thisembodiment, and is therefore also connected to r.f. receiver anddetection circuitry 15 for detecting nuclear quadrupole responsesignals.

A single coil, e.g. an Archimedean spiral coil or a surface coil, may beused (in which case the attenuator 26 may be omitted to simplify theapparatus), but the provision of at least two coils producing differentfield patterns, and means for adjusting the amplitude of exciting signaldelivered to each coil offer more flexibility in varying the fieldstrength pattern; the minimum and maximum field levels, corresponding tothe minimum and maximum flip angles for a given pulse length, mayreadily be set to desired values. One skilled in the art will be awarethat computer programs which calculate field patterns for given coilpatterns and enable deduction of an appropriate coil configurationcapable of producing a desired field pattern are readily available. Forexample, software entitled “Mega” which is commercially available fromBath University, England has been used to determine the coilconfigurations necessary to produce the field patterns required inMagnetic Resonance Imaging.

Variation in Field Strength

In this embodiment the field strength varies with position so themagnitude of the response signal will be affected, and this must betaken into account. In this embodiment, the control computer 16 isprogrammed to calculate the expected field strength at any particularposition in the vicinity of the sample for a given set of receiverexcitation amplitudes. The precise way in which this is achieved may bevaried. For example, the overall shape of the field pattern may becalculated according to a formula (theoretical or empirically corrected)for the pattern from the coils used. This may be scaled by anempirically determined adjustment factor, based on observed fieldstrength at one or more locations. Alternatively, the spatial variationof the field from the exciter coil arrangement is measured and stored asa look-up table in memory means (which may be a part of the controlmeans 16). Interpolation may be used between stored data points.

Arrangement for Resolving Signal into Two Components

In this embodiment, the detector 15 includes a quadrature detector whichreceives a reference r.f. signal from the phase/amplitude control 10,and produces a real output based on the component of the received signalin phase with the reference signal and an imaginary output based on thecomponent of the received signal having a phase difference of 90 degrees(either lead or lag may be used provided this does not changeunpredictably) to the reference signal. Both of these outputs areseparately digitised, and stored in the computer 16.

In this embodiment, the computer 16 is arranged to obtain the values oftwo components which are phase and amplitude dependent from thedigitised outputs (after sampling for a time preferably at least equalto the Free-induction-decay period) by Fourier transforming the outputsand integrating the resulting waveforms between two points, preferablythe full-width half-power points centred on the peaks found at theresonant frequency. This yields two values (one for each output of thedetector) representative of the magnitude of the response signal; thisarrangement is found to give components with a good signal-to-noiseratio.

However, the arrangement for obtaining the components is not critical,and others may be employed. References throughout this specification totwo components are intended to include, for example, values obtainedfrom the outputs of a quadrature detector by integrating the area underthe Free-induction-decay curve envelope (e.g. by digitising the signal),or by taking the peak value of output signals at a particular instant intime, or by Fourier transforming the received signal and taking the peakvalue or by integrating between two points as mentioned above. Althoughthe output of a detector will usually be sampled for a period of time(e.g. at least the Free-induction-decay time) and a single value foreach component produced from the results of the sampling (to reducenoise), it may be desirable in some instances to obtain a plurality ofvalues for each component, for example over a series of time increments,and references to two components are intended to include time-varyingvalues as well as average or total values. It is, of course, importantto ensure that the components obtained reliably reflect the f.i.d. Thisnormally implies that the “dead time” of the apparatus should be muchshorter than T₂* and the f.i.d. should not be truncated by other(unknown) factors.

It will be understood that there are many ways in which one can obtaintwo values which are representative of both the phase and magnitude ofthe response of a sample. In this preferred arrangement, the resolutionof the signal is implemented at least partly in hardware. However, theresolving function may be incorporated into the function of the controlcomputer 16 or other processing means. Where the data are processeddownstream, the minimum resolving function that needs to be incorporatedin the apparatus itself is the inclusion of sufficient information toenable downstream extraction of phase and amplitude information from thedigitised data.

Control of Variable Parameters

In this embodiment, the control computer 16 also controls all pulses,their radio frequency, timing, duration, amplitude and phase. In thecontext of the present invention all of these parameters may need to beadjusted precisely; for example, the duration and amplitude of thepulses may be adjusted to image different sections of the sample, andphase may be varied in order to resolve distances more accurately.

The computer 16 is also arranged to repeat application of pulses asnecessary to scan or image the region of interest within the sample. Inaddition, in embodiments in which one or more gradients such as magneticfield, electric field, temperature or pressure, gradients aresuperimposed on the sample to assist in imaging or in stress or thermalanalysis, the computer 16 is normally arranged to control (at leastpartly) the imposition of that or those gradients.

Re-tuning of the r.f. probe 14, alteration of its matching andalteration of its Q factor may all need to be carried out dependent uponthe nature of the sample. These functions are carried out by the controlcomputer 16 as follows. Firstly, the computer checks the tuning of ther.f. probe 14 by means of a pick-up coil 18 and r.f. monitor 19, makingadjustments by means of the tuning control 20. Secondly, the matching tothe r.f. power amplifier 13 is monitored by means of a directionalcoupler 21 (or directional wattmeter), which the computer responds tovia a matching circuit 22, which in turn adjusts the r.f. probe 14 bymeans of a variable capacitance or inductance. The directional coupler21 is switched out by the computer 16 when not required, via switch 23.Thirdly, the Q factor of the r.f. coil is monitored by afrequency-switch programme and adjusted by means of a Q-switch 24 whicheither changes the coil Q or alternatively alerts the computer toincrease the number of measurements.

Other Features

This embodiment includes transport means, such as a conveyor belt ormovable platform 27 to move the sample relative to the coil(s), to imageor test different portions of a sample or a succession of samples. Thecomputer 16 may be arranged to time the application of the firstexcitation pulses substantially simultaneously with the arrival of aparticular sample adjacent the probe. Other arrangements for moving theprobe relative to the sample may be used. For example, instead of thesample being carried on a conveyor belt, it may actually be a person,and the r.f. probe may be in the form of a walk-through gateway or ahand-held wand. A movable probe may have means for transmittinginformation representative of the position and or orientation of theprobe relative to a reference position, to facilitate investigation ofan object larger than the probe by moving the probe around the object.

Image Construction and Display Apparatus: Data Processing

The control computer 16 in this embodiment is also arranged to constructan image from the received data, as will be described in more detailbelow. In particular, it calculates a phase parameter from a ratio oftwo components obtained as described above. However, particularly whereimage data are formed from the received signal, the data may beprocessed further (for example for image enhancement or recognition)downstream of the control computer 16.

The results of the testing, in this embodiment, are displayed ongraphical display apparatus comprising VDU 17. The results may bepresented as a profile of the sample, which will indicate where in thesample (e.g. a suitcase) a responsive substance (e.g. an explosive) maybe found. The results may simply be used to produce an alarm if aprofile according to predetermined criteria is found. This may beparticularly useful, for example in detecting sheet explosive inluggage, or may be useful in detection of a bodily tumour.Alternatively, an output representative of the distance of the majorityof the quadrupolar nuclei or of their distribution or of the quantity isprovided. This may be particularly useful, for example, in a modifiedapparatus in which the probe 14 is arranged for determining the locationof underground explosives, or the location of a desired substance in abody. It will be understood that the information obtainable with thisinvention can be used in a number of ways, and with the teachingpresented herein, one can select a method appropriate to a particularapplication.

Other Conditions

Although the apparatus described above would usually employ rectangularpulses, other pulse shapes, for example adiabatic pulses as described inour earlier International Application Number WO 92/21989 may beemployed. Furthermore although usually the radio-frequency probe wouldutilise a single coil for both transmission and reception of signals,any appropriate number of coils may be used, and different coils can beused for transmission and reception.

The apparatus would usually operate in the absence of any appliedmagnetic field. However, in cain circumstances, it may be desirable tosuperimpose magnetic field gradients on the sample, as this may improvespatial resolution. In contrast to NMR imaging, however, the inventiondoes not require a strong homogeneous magnetic field in addition to anymagnetic gradient imposed on the sample. Preferably, the averagemagnetic field in the vicinity of the sample is no greater than themaximum variation in magnetic field strength across the sample.Preferably, the average value of the magnetic field, or the value of themagnetic field minus the peak variation in the strength of the magneticfield is less than 0.1T, and preferably less than about 0.01T, or of theorder of the earth's magnetic field. Preferably, any magnetic fieldapplied to the sample is applied only by means of an arrangement ofcoils which generate a substantially non-uniform field in the vicinityof the sample. Thus, the drawbacks of the requirement with NMR imagingfor a coil arranged to provide a strong homogeneous field can bealleviated.

EMBODIMENT 2

This embodiment, illustrated schematically in FIG. 1B, has a number offeatures in common with the above embodiment; like parts are designatedby like reference numerals and the following description concentrates onthe differences between the embodiments.

The second embodiment is specifically concerned with imaging an object,for example a portion of a person as illustrated.

Coil Arrangement

In this embodiment, the r.f. probe contains 3 sets of coils, and theswitchable attenuator 26 is used to select the field direction as wellas the intensity pattern. Each set of coils comprises an Archimedean (orsimilar) spiral coil at one side of the sample space, and a Helmholtzpair either side (as shown in FIG. 1B, the torso of a patient extendsthrough the centre of one of the Helmholtz coils). Other parts, such asarms, legs, the head or the neck of the patient may be accomodated.

In a further alternative embodiment, not shown, separatereceiver/detection circuitry 15 is provided for each direction tofacilitate overlapping measurements from each direction. Whilst a singlecoil can readily provide profile information in one direction, to form atwo or preferably three dimensional image, information in more than onedirection is required. Three orthogonal coils should theoreticallyenable 3 independent measurements from 3 different directions.

In practice, the measurements are not fully independent, due in part todivergence of the magnetic fields from the coils. Nevertheless, theprofiles obtained in the three directions enable a three-dimensionalimage of the sample to be constructed. Some distortion may be observed,particularly where responsive nuclei are located far from the axes ofthe coils. Thus, for best results, the object of interest (here thethyroid gland) is positioned approximately at the centre of theapparatus, to enable more accurate imaging.

In this embodiment, the amplitudes of signals fed to each coil arecontinuously adjustable by means of adjustable attenuator 26, to enableprecise control of the field pattern. It will be appreciated that,instead of an adjustable attenuator coupled to the output of a singlepower amplifier, a plurality of adjustable power amplifiers may be used,one for each coil; this may have benefits, particularly when largepowers are used.

Processing of Data and Image Display

In this embodiment, where large amounts of data are collected, forexample to produce a high resolution 3-dimensional image, it may bedesirable for the control computer to be arranged to control theapparatus and acquire the data desired, and then pass the data to aseparate processor (e.g. of greater processing power) as raw,partially-processed, or filtered data. Thus the image processingfunction of the control computer 16 may in practice be implementedremotely. The apparatus may include hardware specifically designed toimplement mathematical transforms (e.g. Fourier transforms, Hankeltransforms) to achieve faster image processing. Image constructiontechniques are discussed in more detail below. In variants, as mentionedabove, the image may be subjected to image processing or imagerecognition algorithms before being displayed, and may not be displayedat all.

Where an image is displayed on a visual display unit 17, the unit willnormally be provided with input controls to enable adjustment of theposition or orientation of the portion of sample corresponding to theimage displayed. Adjustment may be achieved mathematically based onpre-stored data, or by adjusting the physical sampling conditions, orboth.

Other Conditions

The frequency used will typically be appropriate for nitrogen nuclei inthe sample, but in some cases other nuclei may be excited. Particularlyin the case of a biological substance containing nitrogen and iodinee.g. a thyroxin analogue, it has been found desirable to select afrequency appropriate to iodine in the substance. Of course, thenitrogen or other nuclei may be detected alternatively or additionallyin some cases. Typical frequencies range from a megahertz or more for¹⁴N to several hundred megahertz for ¹²⁷I, and powers may range from afew watts or less to the order of a kilowatt or more depending on thesample size and location. At higher powers, as will be understood, caremust be taken not to damage the sample, particularly in cases wherepatients or other biological specimens are investigated.

Other Coil Arrangements

The above exemplary embodiments may be modified in a number of ways tosuit the application of interest. Other possible coil arrangementsinclude generally conical or frusto-conical coils, Helmholtz oranti-Helmholtz pairs, or combinations of the above. It will beappreciated that the field from a coil tends to vary approximately as afunction of r⁻³ (where r is distance from the coil) near the coil, andas a function of r⁻¹ at large distances from the coil. For example, fora circular coil of radius a, the field is proportional to(r²+a²)^(−3/2), which approximates to r⁻³ when r>>a and r⁻¹ when a>>r.

One or more coils may be connectable in antiphase to other coils (sothat the fields subtract rather than add); this may be used to producesubstantially zero net field (i.e. zero flip angle) at one or morepredetermined locations in the sample.

Concentric coils may be employed for depth profiling, as the field depth(rate of decay with distance) will vary as a function of coil size. Ifthe coils are eccentric, then the depth and centres will vary; such anarrangement may be used to produce further information regarding thedistribution of nuclei for cross-checking or comparison with informationobtained by the basic method described below.

One or more coils may comprise a plurality of coil elements, and thecoil configuration, that is the effective shape of the coil, (forexample a generally meanderline coil) may be adjusted by switchingelements into or out of circuit.

Arrangement for Determining Position by Triangulation

In addition to the above, or separately, the position of responsivenuclei may be determined by the triangulation method discussed below. Apreferred coil arrangement for implementing this will be brieflydescribed.

Two (or more) receiver coils are used to detect the signal resultingfrom excitation from a separate transmitter coil. The received signalstrength at each receiver coil will vary as a function of distance(normally αr⁻³), and this can be used to determine the distance of theresponsive nuclei from each coil and hence their position (or otherpositional information) by triangulation using reference points based onthe position of the receiver coils. The phase of the resulting signalshould give an indication of the distance from the transmitter coil, ifthe excitation is chosen as described below, and this can provide afurther reference point.

In other arrangements for determining positional information bytriangulation, two or more transmitter coils are employed, and used inthe determination of distance from each transmitter coil.

As a further arrangement, a single receiver/transmitter coil may bemoved with respect to the sample.

TECHNIQUES FOR NQR TESTING AND IMAGING

Introduction and First Embodiment of the Method

Having described the apparatus, methods which may be employed inembodiments of the invention will be discussed, together with a brieftheoretical explanation. In a first embodiment of the method of theinvention, two radio-frequency pulses comprising a “spin locking” (S.L.)type sequence are employed. This has the benefit not only of producingtwo detectable components, but also of locking the magnetisation fromthe first pulse, which can improve the signal to noise ratio and reducespurious signals.

As is well known, the flip angle produced by a single pulse will beproportional to the product of the amplitude B₁ of the pulse and theduration T of the pulse, i.e. α=kB₁T, the constant of proportionality kbeing dependent on the magnetic moment of the nuclei and containingother factors which depend on the nuclear spin quantum number I of thequadrupolar nucleus.

The basic technique for exciting phase and amplitude components is touse an initial pulse of nominal flip angle 90° and phase 0° (termed a“90°_(0°)” pulse) to rotate the magnetization into parallelism with(say) the Oy axis of the rotating frame (M_(o) lies along Oz and B₁along Ox). This pulse is then immediately followed by the spin lockingpulse of equal length and a phase shifted by 90° with respect to thefirst. Hence the combination of the two pulses can be written in theform (90°)_(0°)-(90°)_(90°). The combination of two or more pulses issometimes known as a sandwich or composite pulse. However, herein,throughout, the combination is regarded as two distinct pulses. It willbe appreciated that, as discussed further below, the flip angle may varythroughout the sample, and hence a pulse referred to as having a nominalflip angle of 90 degrees may in fact produce quite different flip anglesat different points in the sample. For ease of understanding, the caseof a single flip angle will be discussed first.

The second pulse has the effect of locking the magnetisation produced bythe first pulse. In addition, according to the theory developed pursuantto the invention (presented throughout purely by way of explanation toassist in understanding the invention, and not to be construed aslimiting in any way) the second pulse will also rotate the residualmagnetisation, i.e. that remaining unaffected by the first pulse ontothe Ox axis. Thus the net magnetisation should lie somewhere in the x-yplane (of the rotating frame), the position being dependent on thedegree to which the magnetisation was rotated by each pulse. Accordingto the present theory, this orientation should be detectable as thephase of the resulting signal, or the ratio of the real and imaginarycomponents of the received signal (corresponding to the outputs of theresolver 15).

The outputs of quadrature detector 15 comprise two signals obtained fromthe system responses oscillating at or close to the resonant frequencyof the nuclei under test, and decaying according to thefree-induction-decay (f.i.d.) time. These signals may be used to providetwo components directly, preferably by passing them through a peak valuedetector or a low-pass filter or by digitising and then integrating, butas discussed above, values for the components are preferably obtained byFourier transforming the outputs. The results obtained in practice showa phase offset.

Of course observation of a single phase offset does not necessarilyconvey information, and prior to the invention one would attribute aphase offset to arbitrary delays in the apparatus, but notrepresentative of any information concerning the sample itself.

According to the present theory, this phase offset is not an arbitraryquantity; as well as a constant instrumental offset, there is onerepresentative of the orientation of the spins following two pulses.

Surprisingly, it has been observed that phase encoding is possible inNQR testing, even in the absence of a magnetic field, if the excitationis suitably chosen; the phase can be made to vary in a predictablemanner as a function of flip angle.

Variation of Flip Angle

Referring now to the subsequent figures, the effect of varying the flipangle will be explained in more detail, firstly theoretically, and thenwith reference to actual results; this demonstrates that the observedphase of the response signal is indeed a predictable function of flipangle and not merely a result of delays in the apparatus. As discussedfurther below, variation in flip angle due to a non-uniform field may beused to obtain positional information from the phase of the detectedsignal. The differing phase shifts produced by differing flip angles mayalso be used in the reduction of noise.

FIG. 2 shows the expected NQR signal intensity as a function of pulselength following a single on-resonance r.f. pulse for a polycrystallinesample. As is well known, the signal has a single phase and theintensity has a Bessel function dependence. This graph is plotted forconstant field strength. It will be understood that a similar graph maybe obtained if the pulse duration is kept constant, and the fieldstrength varied. If the field strength varies with position, then theamplitude of the signal will give an indication of position ofresponsive nuclei; this is the principle employed by Rommel et al. inthe paper mentioned above.

Surprisingly, a hitherto unreported phase dependence of the responsesignal (from a polycrystalline sample) has been observed followingexcitation with two consecutive (on resonance) pulses (e.g. of equallength) differing in phase by 90 degrees. According to the presenttheory, assuming that some of the magnetisation is rotated from e.g. thez direction into the x direction (in the rotating frame) following apulse along the y direction, the response signal from a polycrystallinesample of spin I=1 (as a function of pulse length) following twoconsecutive pulses of equal length differing in phase by 90 degreesshould be as shown in FIG. 3. As can be seen, the expected signal hasreal and imaginary components. These are the two components produced bya quadrature detector, and can be considered to be the components alongthe x and y axes of the rotating frame. If x and y are the twoquadrature components, then the phase φ and magnitude A of the signalare given by the equations:

A ² =x ² +y ²  (1)

and

tan φ=x/y  (2)

It has been observed that the real component x varies as J(α) and theimaginary component y varies as J(2α), under the experimental conditionsdescribed above (equal length pulses for a polycrystalline sample ofspin I=1). Where this is the case, the phase and magnitude can also beexpressed as known mathematical functions. FIG. 4 shows the sameinformation plotted as phase parameter (x/y) and magnitude information.

The phase difference of the two exciting pulses need not be exactly 90degrees, but a difference of 90 degrees facilitates discrimination ofthe two components and allows the second pulse to lock the magnetisationproduced by the first. Other phase differences may be used and stillenable useful information to be gleaned from the phase of the responsesignal. In some cases, other angles for example in the range 30°-150°,better 45°-135°, and more preferably 60°-120° or 75°-105° may beemployed. As discus below, the pulse durations need not be equal.Furthermore, other features of the excitation may affect the phase ofthe response signal (for example using off-resonant excitation) and thusalthough excitation with two pulses is particularly preferred for itsease of implementation and readily predictable results, other excitationmay be used.

The graphs of FIGS. 3 and 4 are clearly multi-valued over the range ofpulse lengths considered. However, if the pulse lengths and/or fieldstrengths are varied so that the total flip angle lies in the range 0 to2π (0-360 degrees), and the same data plotted as a function of flipangle, the results can be seen in FIGS. 5 and 6 (in which FIG. 5 is aplot of real and imaginary components, and FIG. 6 is a plot of phaseparameter and magnitude). Thus, if the flip angle is varied in the range0 to 2π throughout the sample, the phase will be a single-valuedfunction of flip angle. Reference is made above to phase. In fact, aphase parameter which need not actually be phase may be used inpractice. In particular the ratio of the real and imaginary components(x/y) may be used as a phase parameter as this is easy and fast tocalculate (it does not require calculation of arctangents). FIG. 7 showsclearly that the ratio of the expectation values of the real andimaginary components (a phase parameter) displays a monotonic change inthe range of flip angles 0 to 2π.

Obtaining Positional Information or Imaging

As will by now have become apparent, if the flip angle varies throughoutthe sample, the resulting phase (or phase parameter) will give anindication of position. Thus, in a development of the first embodiment,the magnitude of the exciting B₁ field varies with position throughoutthe sample in a predetermined manner, this being achieved by appropriatechoice of transmitter coil or coils 14, as discussed above in relationto the apparatus. By selection of the range of maximum and minimum B₁field values, together with appropriate pulse durations, the range offlip angles in a sample, or in a region of interest, and hence theexpected phase angles can be controlled.

From the field at a given position, the pulse duration and the constantappropriate to the nuclei under investigation, the flip angle at a givenposition can be calculated. If the flip angle varies within the samplein the range of 0 to 2π, the position of a crystal of responsivematerial within a larger sample can thus be obtained from the phase ofthe peak corresponding to that crystal by determining the correspondingflip angle from the graph shown in FIG. 6 (or from the ratio of the twoquadrature components with reference to FIG. 7), and relating this toposition according to the field variation. If the flip angle exceeds 2π(corresponding to high field strength, near the coil), then it isnecessary to use data based on the appropriate segment of the graphs ofFIGS. 3 and 4, in which the phase will not be a single-valued functionof position. Nevertheless, the position can still be obtained, by takingmultiple measurements to resolve any ambiguities. Additionally oralternatively, the amplitude of the signal may be used to give anindication of the appropriate position on the graphs to consider; theamplitude will vary with position, almost invariably diminishing withdistance from the probe, in a known manner.

By way of further example, a plot of ratio of the quadrature componentsproduced by detector 15 against distance is plotted in FIG. 8 for afield which varies according to an inverse cube law in the vicinity of alocalised sample. Note that this curve is effectively obtained from thatof FIG. 7 by inversion (low flip angles correspond to large distances)and expansion in the horizontal direction by a variable factor (thecurve is compressed at points near to the coil, where the field strengthchanges rapidly with distance, and expanded further away from the coil,where the rate of change of field with distance is much lower). Thus,from this graph, an approximation appropriate to a probe comprising anArchimedean spiral, the distance of a crystal from the probe may bedetermined directly from the ratio of the components after simplecalibration of the apparatus to take into account the size of the coiland any inherent phase delays.

The magnitude of the resulting signal gives an indication of the totalnumber of nuclei present in the sample. For a more accurate indication,this should be adjusted to take into account variations in the excitingfield strength at different positions in the sample. Where a transmittercoil 14 producing a field which diminishes with distance from the coilis also used as a receiver, account must be taken of the fact that thereceiver will be correspondingly less sensitive to signals originatingfrom further away; this will be true in most practical applications. Asdiscussed above, adjustment may be achieved by storing data relating tothe variation of field and receiver sensitivity with position andscaling the amplitude data according to the position from which itoriginates.

From the quantity and positional information, a profile of thedistribution of responsive nuclei can be obtained.

The resonance frequency of a nucleus is affected by the localenvironment, as is well known in the art. If variations in resonancefrequency are measured (for example by repeating the experiment for avariety of exciting frequencies), an output of this information togetherwith the positional information may provide a profile of variation of afactor such as temperature pressure or stress which affects theresonance frequency. It will be apparent that this may be useful inthermal or stress analysis.

Experimental Results for ¹⁴N NQR in RDX—Single Cluster of Nuclei

Turning now to some experimental data, FIGS. 9-11 show the real andimaginary components obtained for single 200 g polycrystalline samplesof RDX centred at distances of 6.9, 9.9, and 14.9 cm respectively from a25 cm diameter spiral coil (with spacers of 2, 5, and 10 cmrespectively); these results were obtained using the spiral coil of theembodiment of FIG. 1A to excite the sample. On resonance pulses of equallength with a phase shift of 90 degrees were used, and the 5.19 MHz linewas observed.

Firstly, it can be seen that at greater distances from the coil(corresponding to lower field strength), a maximum amplitude occurs atlonger pulse lengths, since at lower field strengths, the flip anglevaries more slowly with variation in pulse length. This dependence ofthe pulse length for maximum amplitude on position is the basis for themethod of Rommel et al. discussed above.

With the plot of real and imaginary components, it can also be seen thatfor a given pulse length (e.g. 100 μs) the relative sizes of the realand imaginary components are different for each position, thus the phasewill also be different for each position of the sample, as explainedabove, so the position of a single sample may be determined from thephase of the signal.

Referring now to FIG. 12, a phase parameter (ratio of real and imaginarycomponents) is plotted as a function of pulse length for samples at twodistances from a spiral coil; the square points correspond to the dataof FIG. 9 and the circles correspond to the data of FIG. 11. The phaseparameter has not been corrected to take into account phase delays inthe apparatus (this is discussed below). Nor has it been filtered orrepeated to reduce the effect of noise, or to take into account thediminished signal magnitude obtained from the sample further away.Nevertheless, it can clearly be seen that the curves exhibit a phasedependence generally similar to that predicted in FIG. 7.

Concentrating first on the square data points, it will be seen that theratio of the real and imaginary components changes smoothly up to apulse width of approximately 150 micro seconds. Referring now to thecircular data points, it will be seen that there is little change in thephase parameter until a pulse length of about 350 micro seconds; this isbecause the sample is further from the spiral coil, so the field iscorrespondingly smaller and hence the flip angles (proportional to theproduct of field and duration) are small. It will be appreciated thatwhere one component has a small magnitude (e.g. at low flip angles), theeffect of noise will be greater.

It may be seen that the traces obtained do not correspond exactly tothose discussed above. This can be attributed to a phase delay in theapparatus (for example in the power amplifier or detector). The phasedelay results in the measured real and imaginary components beingrelated to the “theoretical” real and imaginary components according tothe well-known equation for rotation in the complex plane by a phaseangle β equal to the net phase-shift in the apparatus. That is, if the“theoretical” components are x+jy, the observed components x′+jy′ shouldbe given by the equation x′+jy′=(x+jy)(cosβ+jsinβ). The phase-shift fora given apparatus can be determined empirically and the data transformedbefore calculation is performed, or it can be taken into account in thecalculation. Alternatively, the phase offset for the apparatus can bedetermined by comparing the measured and predicted response signals fora variety of flip angles. In the majority of results presented herein,the phase of the apparatus was pre-set by performing an initialexperiment with a nominal 90° pulse and adjusting a variable delayinserted in the signal path to the quadrature detector to give a maximumvalue for the real component.

It will be understood that if the flip angles in the sample lie in therange of 0 to 2π, the measured phase (i.e. including the phase shift)should still be a single-valued function of flip angle (and henceposition) but will be offset from that depicted in FIG. 6, and may notbe monotonically increasing or decreasing.

It will be apparent that for typical frequencies used (a few MHz), thesignal wavelength will be of the order of a hundred meters, and sounless the sample is very large, the phase shift can be assumed to beconstant throughout the sample; adjustment of measured phase shiftstaking into account phase shifts due to propagation delays may be madeif desired.

In the above experiment, a large number of pulse lengths were used for arelatively small number of sample distances from the coil, todemonstrate the effect of flip angle on phase of the received signal.This was for experimental convenience; it is easier to produceconsistent results rapidly if pulse length is varied than if the sampleis physically moved. As discussed above, particularly with reference toFIG. 8, similar results would be expected if phase parameter wereplotted against distance; effectively the curve of FIG. 12 would bestretched in the x-direction by a variable factor dependent on the fieldpattern produced by the coil.

It will be appreciated that for a known coil field pattern, the distanceof one object from the coil can in principle be determined fromexcitation with a pair of pulses. In practice, to compensate for theeffects of noise, and to extend the useful range of distances, it isdesirable to adjust one or more of the field strength and pulse durationso that the measured phase parameter can provide an accurate indicationof position. For example, referring to the square data points in FIG.12, and using the same field strength, a pulse length of 80-100microseconds would be appropriate as this would lie on a region of thecurve in which phase changes predictably and smoothly with distance; forthe circle data points, a longer pulse length would be better and/or(more preferably) a higher field strength (e.g. about 5-10 times theamplitude) would be used to reduce noise.

A more accurate determination can be made by measuring the phaseparameter for a number of pulse durations and preferably for severalfield strengths, and then fitting the resulting data to an appropriatecurve; this will reduce the effect of spurious measurements. Theresolution will increase as more pulse durations are selected.

It will be appreciated that many variations of this method may be usedto obtain effective position determination over a range of distances;for example an initial series of measurements may be taken to determinean approximate position for a sample, and then further measurements maybe taken to refine the position determination.

Thus, it can be seen that the data encodes the position of a sample withrespect to the coil. This data can be processed in a number of ways,depending on the results required. Two methods which can conveniently beused to obtain an image from the data will now be described.

First Image Derivation Method—Best Fit Method

One way in which an image or other representation of the sample can beobtained from the data is by fitting the experimentally acquired data toa theoretical prediction of data to be expected for a particulardistribution. The basic scheme for performing the method is:

1 Acquire data from real sample.

2 Initialise variables controlling model (for example depth of cluster,width of cluster).

3 Predict results expected for model.

4 Compare predicted to actual results.

5 Vary model parameters.

6 Repeat steps 3 to 5.

The first 3 steps may be performed in any order. The repetition isperformed until the desired resolution is obtained. Comparison may beperformed by visual matching of data, but is best performed numerically,for example by use of a χ² test. This technique is best suited togeneration of a simple image, or where the sample is expected to havecertain properties corresponding closely to a relatively simple model. Aparticular use is in the determinination of the position and approximatesize of a single cluster of material, for example in the screening ofluggage for explosive, or the detection of underground explosives.However, if the data is acquired with a sufficient signal to noiseratio, complex models can be fitted to the data.

In more detail, the model may be predicted by assuming that the realcomponent varies as a function of J(α) and the imaginary component as afunction of J(2α), where α is the flip angle. The flip angle may beassumed to have a particular dependence on distance from the coil, forexample inverse cubic, or may be based on an empirical determination.The model is preferably calibrated, by reference to known samples.

Where a calculation is performed assuming a relatively uniform sample ofa given thickness at a certain distance from the coil, it is preferredto vary the assumed distance first to obtain an approximate fit, andthen vary the assumed thickness, and then if necessary to adjust thedepth; this provides an efficient means of localising a sample rapidlyand reliably.

Referring to FIG. 16, a comparison of predicted results with actualresults obtained from a 6 cm wide sample of RDX 7 cm from a coil areshown. In the plots, the dash-dot line represents the measured realcomponent, the short dashed line represents the measured imaginarycomponent, the dashed line represents the predicted imaginary component,and the dash-dot-dot line (or in FIGS. 16c and 16 d, the long dashedline) represents the predicted real component.

As can be seen, a good fit is obtained when the model parameters arecorrect, as in FIG. 16a. When a small change is made in the predicteddistance (to 6.5 cm or 8 cm), the fit becomes noticeably less good quiterapidly, as can be seen in FIGS. 16b and 16 c. However, as can be seenfrom FIG. 16d, it is less easy, though possible, to discern smallerchanges in sample size by visual matching of curves.

Thus, the fitting is preferably performed numerically. A measure of thegoodness of fit plotted as a function of one or more model parameterssuch as distance can be plotted. Alternatively, a numerical output ofthe most likely sample size and dimensions can be produced. FIG. 17shows the results obtained by performing a chi-squared fit of themeasured to the predicted data and plotting probability (1/χ²) againstdistance for a sample located 2.7 cm from a coil; a clear peak can beseen at the “correct” distance.

As will be appreciated, the above one-dimensional experiments can beperformed along three orthogonal directions and an image formed byprojection-reconstruction, or an image can be formed by moving thesample with respect to the image.

Second Image Derivation Method—Fourier Transform

As mentioned above, the first method is best suited to generation ofimages of simple samples. There will now be described a method which hasbeen successfully used to resolve multiple clusters of nuclei.

Following the procedure of Rommel et al (Meas. Sci Technol; 1991, 2,866-871, incorporrated herein by reference), a double Fourier transformis performed with respect to the FID time t and the “pseudo-FID” time(or pulse length) tp. After the first, on resonance, we have theequivalent of Rommel's equation (5) as $\begin{matrix}{{S\left( {\omega,t_{p}} \right)} = {e^{\frac{- {({\omega - \omega_{\varphi}})}^{2}}{2\quad \delta}}{\int_{- \infty}^{\infty}{{\rho (z)}{M\left( {t_{p},z} \right)}\quad {z}}}}} & (1)\end{matrix}$

in which p(z) is the number density of resonating nuclei and δ is theNQR line second moment. Following the explanation presented above, themagnetisation M(t_(p),z) can be written as $\begin{matrix}\begin{matrix}{{M\left( {t_{p},z} \right)} = {{x\left( {t_{p},z} \right)} + {{iy}\left( {t_{p},z} \right)}}} \\{= {{J(\alpha)} + {{iJ}\left( {2\alpha} \right)}}}\end{matrix} & (2)\end{matrix}$

where

α=2γB ₁ tp=2γG _(z) zt _(p)  (3)

in a linear B₁ gradient of G_(z). Hence equation (1) can be written as(omitting constant terms)

S(ω,t _(p))=∫_(−∞) ^(∞)ρ(z){J(α)+iJ(2α)}dz  (4)

Under certain conditions, Rommel et al show that the Bessel function(Jα) can be written as $\begin{matrix}{{J_{1}(\alpha)} = {{\sqrt{\frac{2}{\pi \quad \alpha}}\sin \quad \left( {\alpha - \frac{\pi}{4}} \right)} + {O\left( \alpha^{- 1} \right)}}} & (5)\end{matrix}$

Combining equations (4) and (5) and performing a second Fouriertransform with respect to t_(p), or in k component space, k_(z), where

k _(z)=2γG _(z) t _(p)  (6)

gives us the profile ρ(z)

ρ(z)=F _(k) {S(ω,k _(z))}  (7)

to a reasonable approximation. The distance dependence of thesensitivity σ(z) then gives us the true or corrected profile.

ρ(z)_(coπ)=ρ(z)/σ(z)  (8)

In a two-dimensional representation, the profile information ispresented along the td⁻¹ (or K_(z) ⁻¹) axis and spectroscopicinformation along the t⁻¹ axis, so that more than one NQR transition canbe imaged at the same time.

The use of both phase and amplitude information in the spectrum meansthat the method presented here has a higher sensitivity than theamplitude encoding technique of Rommel et al. FIG. 6 shows that themagnitude of the magnetisation is largely independent of α for α>0.5(below this value, an additional correction will need to be made). Thisis even less of an approximation for the pulse sequence used in theresults presented in FIG. 14, in which the overall pulse length wasconstant, so that the width of one pulse is increased by as much as theother is diminished.

In outline one scheme for performing the method is:

1 Acquire a set of time domain data for a starting value of pulselength, t_(p)

2 Increment the pulse length and repeat step 1 to obtain an array ofdata for a series of values of t_(p)

3 Fourier transform the data with respect to time to obtain a set offrequency domain data for each value of t_(p)

4 Fourier transform the data with respect to t_(p) to obtain pseudo FIDdata; the transformed t_(p) axis will now correspond to a function ofdistance

5 Select a line of data at a desired value of frequency (for example aresonant frequency of the nuclei); this will correspond to a profile ρ

6 Scale the transformed t_(p) axis to correspond to distance from thecoil (based on equation 6 above, and preferably employing empiricalcalibration)

7 Correct the height of the curve based on the sensitivity of the coilas a function of distance.

FIG. 18 shows the results of performing the above method for threesamples at distances of approximately 2, 7 and 16.5 cm from the coil.The distance axis has been scaled based on empirical calculation, andthe positive portion of the real component of the profile ρ has beentaken plotted, which represents a measure of the amount of material.

In the above described experiment, the pulse durations were equal andthe field strength and pattern were kept constant, and Fouriertransforms were used. Fourier transforms are only an approximation;better results may be achieved by using Hankel transforms (using aseries of Bessel functions in place of sine waves), or by using aMaximum Entropy Method. These latter methods are somewhat morecomputationally intensive, but can readily be performed withoutunacceptable delay on, for example, a standard PC with a 200 MHzprocessor.

Analogous results may be obtained by varying pulse magnitude in place offlip angle. It is also possible for multiple sets of data to becollected with different field patterns, and for the different resultsto be combined, to obtain optimum resolution throughout a large sample.As will be understood from the above, the approximation that the B₁field has a linear gradient G_(z) will have to be adjusted to take intoaccount the variation of B₁ with distance.

It is not necessary for both excitation pulse durations to be equal,although this may simplify data processing. If the relative pulsedurations vary, more complex processing can be performed, using afurther parameter, such as the ratio of pulse durations, or separateparameters for each pulse duration. In place of selecting a singlefrequency and plotting the profile at that frequency, athree-dimensional plot may be produced; this will show variation offrequency with position, and may be used, for example, in obtaining ameasure of temperature distribution within a sample.

In both cases a two-dimensional image may be built either by the use oftwo orthogonal surface coils, or by performing the discrete Fouriertransform (7) along a series of z-directions obtained either by stepwiserotation of the sample about an axis perpendicular to z, or by a similarmotion of the antenna, as already described above.

The above discussion has concentrated on the use of a single spiral coilto transmit and receive signals. The spiral coil, as mentioned, producesa field diminishing according to an inverse cube law. This results in alarge field near the coil which rapidly becomes very small. A potentialproblem with this is that, if it is desired to probe samples far awayfrom the coil with a high signal to noise ratio, a very large field nearthe coil is required, which can require costly high power amplifiers,and may result in excessive power being dissipated in objects nearer tothe coil.

Although the results obtained show that a single coil may besatisfactory for many applications, it will be recalled that the probe14 of the embodiment of FIG. 1A has 2 coils, a spiral coil and aHelmholtz pair (variants have other coils).

A solution to the above-mentioned potential problem is to apply aproportion of the r. f. signal to the Helmholtz pair. This raises theminimum field strength, and so the field strength required from thespiral coil is reduced. By appropriate selection of the proportions, adesired field pattern can be attained in a region of interest of thesample. For example, the field pattern may be set so that throughout thephysical space accessible between the coils, the phase parameter variessmoothly between readily measurable limits for a given pulse length.

Referring back to the imaging method of Rommel et al discussed above, itwill be recalled that positional information was obtained by fitting theamplitude data to a Bessel function. It is clear that fitting data to aBessel function, which has an ill-defined peak, is both moremathematically intensive and likely to be less precise than simplydetermining a phase parameter and cross-referencing this to anappropriate distance, based on a graph or look-up table appropriate tothe pulse lengths and field strengths employed for the coil used.However, an indication of the position of responsive nuclei may bedetermined based on the amplitude of the response signal by a methodsimilar to Rommel's, and the results refined or adjusted by using anindication of the position based on the phase of the response signal.

It should be noted that neither this embodiment nor the invention as awhole are limited to determination of position itself; other positionalparameters, for example including velocity, acceleration etc., may bemeasured. Where velocity is measured, the doppler shift in resonantfrequency may also be taken into account.

Samples Containing Multiple Clusters—Processing Data

For ease of understanding, the above explanation has concentrated on thecase of a single cluster of responsive nuclei. However, the techniquecan equally be applied to samples containing multiple clusters. Wherethere are two or more well-spaced clusters, as in the case of FIG. 12,it will be apparent that at short pulse lengths the cluster further fromthe coil will have little effect, and so the majority of the signal willbe attributable to the cluster closer to the coil. Once the nearercluster is identified, the effect of that cluster on the results can becompensated for to identify further clusters. By adjustment of fieldpattern, the excitation can be arranged so that distinct responses canbe identified for each cluster; this is simple to implement, and workswell for well-defined spaced clusters of nuclei.

Referring to FIG. 13, which is a plot obtained from two samples,positioned at 5.2 and 14.9 cm respectively from the coil, two peaks canclearly be seen on the plot of real and imaginary components. Byanalysing this into a plot of amplitude as a function of phase, adistribution can be determined in which the two samples can bedistinguished. To characterise the distribution better, which isparticularly useful when investigating a sample containing manyresponsive nuclei at different positions, data are obtained for avariety of pulse lengths and/or field strengths.

In general, the greater the number of repetitions (with different pulselengths or durations), the better will be the resolution attainable. Itwill be appreciated that for species which have an f.i.d. time of theorder of a millisecond, 1000 repetitions can in principle be carried outin a few seconds; for substances which have much longer f.i.d. times,the number of repetitions will be a compromise between the timeavailable for measurement and the resolution required.

It is common practice in NQR experiments to repeat each experiment anumber of times (often several hundred times) and average the results toreduce noise. In cases where a number of pulse lengths or amplitudes areused, the measurements for each pulse length or amplitude may berepeated in addition to repeating the measurements for different pulselengths or amplitudes. However, it will be appreciated that this maysubstantially increase the measurement time required; if 500 differentpulse lengths are used, and each experiment is repeated 500 times,250,000 experiments are required. To reduce the total number ofexperiments, experiments which initially produce data having a highersignal to noise ratio (for example at a large excitation amplitude) maybe repeated less often than those which are more susceptible to noise(for example at a lower excitation amplitude). Noise can also be reducedby appropriate combination of data from experiments using differentpulse lengths or amplitudes; for example if the processed data areplotted as points on a graph indicating quantity of nuclei at variouspositions, a smooth curve through the points will tend to reduce theeffect of spurious data from individual points. Similar effects can, ofcourse, be achieved numerically.

For samples in which clusters of nuclei are closely spaced orcontinuous, or for imaging, other techniques may be used to obtainprofile information. Numerous well-known mathematical methods aresuitable for analysing the data to produce a distribution consistentwith the data. The principle used (as used in other imaging methods) isthat the response data obtained for a variety of conditions (e.g. flipangles) are assumed to be the sum of a series of response signals fromdifferent amounts of nuclei at different positions. The amounts ofnuclei which would give the data observed are then calculated by a knownmethod. Examples of suitable methods include the Maximum Entropy Method(MEM), the Fourier transform, and the Hankel transform. Furtherdiscussion of these techniques with specific reference to NQR data maybe found in the paper by Robert et al. entitled “On the Reconstructionof NQR Nutation Spectra in Solids with Powder Geometry” in Z.f.Naturforsch. 49a, 35-41 (1994). U.S. Pat. No. 5,229,722 (discussedabove) discusses methods of constructing images from NQR investigationsand these may be applied to the data obtained with the presentinvention. Of course, it will be understood that complex rather thansimple transforms are appropriate for use with the complex (real andimaginary) data produced by the present invention, but the samemathematical principles apply.

In particular, the method of Rommel, Kimmich et al. discussed above maybe employed, with the advantage that the phase information may be usedto lessen the effect of interference spikes or other spurious signals.In addition, since two values are obtained simultaneously they are notaffected by changes over time of other parameters, so are bettercorrelated and hence may provide better reduction of noise than twovalues obtained simply by repeating an experiment using amplitudeinformation alone. Thus, the phase information enables a more accuratecharacterisation to be obtained than by using amplitude informationalone.

Although the acquisition methods and apparatus of the invention arequite different to those used in NMR imaging experiments, the resultingdata which has phase and amplitude information has similarities. Thus,many well-known NMR image construction techniques may be applied oradapted to the data obtained from an NQR experiment with this invention.An important consideration is that NMR response signals generally havesinusoidal dependence on flip angle, whereas, in the methods of thepresent invention, the resulting signals generally have Bessel functiondependence; thus, where Fourier transforms (series of sinusoids) areemployed in NMR data-processing, it will usually be appropriate to use acorresponding Hankel transform (series of Bessel functions), as will beunderstood by one skilled in the art.

Particularly useful NMR imaging techniques are discussed by Mansfieldand Morris in “NMR Imaging in Biomedicine”, Nature 242,190 (1973), andother discussion is found in J. Magn. Reson. 33,183 (1979).

In particular, methods for determining the location of nuclei in asample by NQR may be based on an adaptation of phase-encoding techniquespresently used in NMR imaging, but previously thought unworkable in NQRexperiments. For example the technique described by Styles in NMR Basicprinciples and Progress, Vol. 27, pages 49-52 employs a series of pulsesin which successive results are summed to generate a maximum signalcorresponding to a desired location.

Obtaining Multi-dimensional Information

As mentioned above, the apparatus of the embodiment of FIG. 1B contains3 orthogonal coils. Thus, to obtain 3-dimensional information about theposition of nuclei in a sample, the measurements may be repeated for 3different directions, and the results combined using known techniques todetermine the three dimensional distribution of nuclei in the sample;although the profile information for one direction is obtained accordingto the invention based on the NQR response of the sample, the resultingprofile data may be processed using known techniques generallyapplicable to processing of profile data obtained by other techniques(e.g. NMR, X-ray CT, ultrasound). It should be noted however that inthis particular application, although the profiles obtained from eachdirection should be substantially independent, in practice someinterdependency is observed due in part to divergence of magneticfields. A similar problem occurs in MRI where surface coils are used,and known techniques for compensating for this in software using wavelettransforms exist. In the Quadrupolar Resonance Imaging of the invention,analogous techniques can be applied, but in this case the correctionmust take into account the fact that the signal depends on B₁ ratherthan the components of B₁ perpendicular to B₀. Alternatively, this couldbe compensated for by obtaining further data from other directions, forexample by rotating the probe relative to the sample, or most simply bykeeping the size of the sample small in relation to the size of thecoils.

Where orthogonal coils are used, excitation and measurement from eachdirection may be sequential (i.e. excitation and measurement completedfor one direction before measurement for another direction iscommenced), or may be interleaved.

In variants of the basic technique described above, alternatively oradditionally, the sample may be moved with respect to the coil(s). Infurther variants, a gradient (e.g. a magnetic field gradient) may beimposed upon the sample; this may be used to assist in resolvingpositional information in one or more directions, or may provide thesole means of resolving information in a particular direction.

As a further alternative, there may be physical movement between theprobe and the sample, as discussed above, and this may be used toconstruct a multi-dimensional (e.g. three-dimensional) image fromseveral profiles obtained at different orientations or positions.

The triangulation method discussed further below may advantageously beemployed to improve the measurement of position.

Refinement of Data

It has been mentioned that a variety of pulse lengths or field strengthsmay be employed to probe different parts of the sample, or to minimisethe effect of spurious signals. However, the above discussion hasfocused on excitation using a pair of pulses of equal duration. Once anapproximate distribution has been obtained using the above method, itmay be desirable to refine this, by making further measurements. Asimple way of improving the accuracy of the measurement is to repeat andaverage, to reduce the effects of noise and spurious signals. Othertechniques which may be employed will be discussed below.

Pulses of Unequal Duration

Pulses of unequal duration may be employed, to provide further analysisof particular regions of interest. From FIG. 14, which is a plot ofphase and real and imaginary components against first pulse flip anglefor a pair of pulses of constant total duration, it can be seen that ata given total phase shift a particular variation of phase with variationof the first pulse duration is obtained. In that figure, the total pulselength corresponds to a flip angle of 0.7π, the dotted and chain dottedlines are the real and imaginary components, the dashed line is theamplitude, and the phase is indicated by the double chain dotted line.This phase dependence will be different for different total phase shifts(i.e. different positions in the sample), and so nuclei at differentpositions can be further distinguished by investigating variation ofreceived signal with first pulse angle. It can be seen that for thisflip angle (and for flip angles of about 0.8π) the amplitude issubstantially constant, but the phase varies significantly as therelative durations are changed.

Another advantage of using pulses of unequal duration is that the pulselengths can be selected so that a large signal, and hence a largesignal-to-noise ratio is obtained, and discrimination achieved byadjusting relative lengths; this may alleviate the problems of increasednoise encountered at low flip angles when the lengths of pulses of equalduration are adjusted to obtain several measurements.

Detecting Motion

As discussed above, the phase of the response signal will be a functionof position. Thus, if the sample is repeatedly probed, the variation ofphase with time will give an indication of motion of the sample.Depending on the f.i.d. time of the sample, real-time determination ofmotion may be possible. For example, for samples having an f.i.d. of theorder of a millisecond, a few hundred determinations may be made everysecond. Determination of motion may be used to investigate diffusion ofquadrupolar nuclei.

Employing Phase Information to Reduce Noise

In another technique, which may be used with a constant or varying fieldstrength throughout the sample, the relative pulse lengths, or totalpulse length is changed, and signals of a particular phase are selected.This may be used to reduce the effect of spurious signals, and improvethe signal to noise ratio. A technique such as this may be employed innumerous applications in which previously only amplitude information wasused.

In a particularly useful embodiment, the excitation is arranged so thata desired signal (that expected to emanate from a substance of interest,if present) has a first predetermined phase, and the excitation repeatedso that the desired signal has a different predetermined phase. From themeasured phase of the response signal, the desired signal can be moreclearly identified, as the phases of other signals will not have changedin the same manner. This may be used either to enhance or reduce theeffect of a signal having a particular phase “signature” in the netmeasurement. Alternatively, by detecting whether or not a predictedphase shift has occurred, this can be used to detect whether aparticular distribution of nuclei is present.

Three Pulse Sequences—Refinement of Phase Determination

As described above, two pulses can result in a response signal whosephase and amplitude vary in accordance with the position and number ofresponsive nuclei in a sample. If a third pulse is applied (preferablysubstantially contiguous with the first two pulses, or at least beforethe half-life for decay of the net magnetisation produced by the twopulses), this will have the effect of locking the net magnetisationproduced at a particular phase.

It will be appreciated that for the third component to lock the netmagnetisation effectively, the direction or phase of the netmagnetisation must be known. This may be achieved by transmitting a pairof pulses, obtaining an initial value for the phase of the resultingsignal, and transmitting three pulses, the phase of the third pulsebeing selected according to the initial value. This may enable lockingof the net spin, with the benefits of improved signal detection thisprovides.

The appropriate pulse sequence may be identified, using the abovenotation (and remembering that the actual flip angle may differ from thenominal angle of 90 degrees) as (90°)_(0°)-(90°)_(90°)-(P°)_(Q°) where Pis the flip angle of the third pulse, typically greater than 90° andhaving a duration greater than T₂*, and Q is some other angle chosenaccording to the phase of signals to be locked.

In a further development, the third pulse may be used to determine amore precise value for the phase of the resulting signal. For example, afurther value for the phase may be obtained based on the signalresulting after transmission of said three pulses. The further value maybe determined on the basis of an error value based on the initial valueand a detected signal. If the sample contains nuclei clustered about asingle position, for example corresponding to a lump of explosive at acertain depth in the sample, then choice of the phase of the third pulseafter determination of the approximate phase of the signal produced bytwo pulses and subsequent measure of the degree of locking (particularlyif repeated for several values) may enable a more accurate determinationof the phase and hence depth of the nuclei.

Three Pulse Sequences—Phase Stepping

Alternatively (or additionally), the third pulse may be used toselectively lock components of a particular phase or range of phases.This may be repeated for a series of phases or ranges of phase. In apreferred development, the phase of the third pulse is adjusted (forexample in discrete steps e.g. from 0 to 2π, or some subset of thisrange, or possibly greater) as the excitation is repeated.

Each pulse will lock only signals of a particular phase. By repetitiveapplication of further pulses of the same phase as the third pulse, itmay be possible to detect signals limited substantially only to thoselocked. This can be employed to scan for signals of a particular phase,and may be successfully employed to provide a high degree of phaseselectivity.

This may be used to obtain more accurate characterisation of the phaseof the received signal, and, where this is correlated to position, thedepth of resonant nuclei in the sample. Particularly where phase varieswith position, this technique may be used to obtain series of data, eachcorresponding to the signal obtained from different positions within asample. In other words, the third pulse may be used to select slices ofinterest. This may be particularly useful in imaging experiments. Inaddition, it may be useful in reducing spurious signals, since signalsemanating from a region of interest can be effectively isolated fromother signals. Selection of phase may be useful also in noisesuppression as mentioned above.

The number and size of the steps in the phase of the third pulse will beadjusted according to the size of the object and the desired resolution,and on the time available for measurement.

As is well known, the duration of a pulse and the precision at which itsphase and frequency can be determined are related; greater phase orfrequency accuracy requires longer pulses, and this must be taken intoaccount, particularly if a large number of small steps are attempted. Inaddition, it may be difficult to achieve precise control of small phaseshifts using a conventional frequency generator and phase shifter. Thus,if intricate phase control is required, it is preferred to synthesiseexcitation waveforms, for example using a digital memory and fastdigital to analogue converter.

The phase steps need not be uniform, and, particularly where the phaseof the received signal is not linearly related to distance from theprobe (which will be true for many arrangements of magnetic fieldcoils), it may be desirable for the size of the phase steps to vary. Forexample, the phase steps may be arranged so that each corresponds to asubstantially constant step in distance.

Determination of Molecular Environments

The response of quadrupolar nuclei in a sample may be affected byinteractions with other nuclei in the local environment. Some of theseinteractions may happen over a timescale substantially longer than theFree-induction-decay period of the nuclei, in which case they will notreadily be observed. However, if a third, locking, pulse is used to lockthe magnetisation produced by the first two pulses for a time comparableto the period over which the interactions occur, then the interactionsmay be observed. In particular, some interactions may result in slightdeviations in frequency. Closely spaced frequencies are often difficultto resolve by conventional methods, such as Fourier transforming thesampled data. It has been appreciated that the phase of signals that areslightly off resonance will change with time. Thus by applying a thirdpulse to lock the magnetisation for a time comparable to the timescaleof the interaction and then measuring the phase of the resulting signal,similar frequencies can be distinguished.

By repeating the measurements for a variety of locking pulse phases ordurations, characteristic frequencies of molecular interactions may beidentified. The phase of the third pulse may be used to assist inmeasurement of the phase of the response signal. Although the thirdpulse will usually be substantially contiguous with the first two, itmay be transmitted after a delay (preferably less than the time for themagnetisation induced by the first two pulses to decay); this may beused to observe how the phase evolves in the absence of a locking pulse.

For substances with long Free-induction decay times, interactions may beobserved without locking the magnetisation, but simply by applying athird, read, pulse to determine the phase of the response signal after apredetermined time; this will produce an echo pulse from which the phasecan be determined.

Echoes

The phase and amplitude information need not be measured directly, butmay be measured by applying a sequence of (composite) pulses to exciteecho responses, for example based on the techniques taught in BTG'searlier International Patent Application Number WO 93/11441. This may beparticularly useful in detection of biological ¹⁴N, where the observedspectra are broad, and T₂* is short. A phase parameter may be determinedfrom one or more echo response signals. The phase of subsequent echosignals may differ slightly, particularly where the frequency isslightly off resonance, in which case the phase will precess at a ratedependent on how far off resonance the excitation is. This may be usedto investigate small frequency offsets, or to investigate molecularinteractions occurring on a timescale comparable to the timescale overwhich echoes can be measured.

Variation of Temperature, Pressure, or Other Parameters

As is well known, changing temperature and pressure tends to alter theresonant frequency of a species; subjecting the species to a staticmagnetic field tends to alter the frequency and broaden the response forintegral spin quadrupolar nuclei such as ¹⁴N, or to produce a broadeningand/or splitting of the line (in the response spectrum) forhalf-integral spin quadrupolar nuclei such as ³⁵Cl. Shifts intemperature and pressure can thus be determined by altering thefrequency of measurement or by measuring the resonant frequency, andthis combined with positional determination can be used for stress orthermal characterisation. Conversely, if the sample is subjected to aknown gradient, the measurements will depend on position in a knownmanner, and this can be used to provide further positional information.Shifts in frequency or splitting of a spectral line into differentcomponents due to a magnetic field may also be used to measure thefield; this may be useful in analytical applications in which the samplemay contain ferromagnetic contaminants.

Preparation Pulses

Prior to sampling, one or more pulses (at frequencies other than themeasurement frequency) may be applied to the sample to alter thepopulation of nuclei in different excited states. The intensity of theresponse signal is proportional to the difference in populations in eachstate, so if this difference is increased, the response signal will becorrespondingly stronger. For example, if a pulse having a frequencycorresponding to a transition from the first excited state to the secondexcited state is applied, the population of nuclei in the first statewill be reduced and the population in the second state increased.Subsequent measurement at a frequency corresponding to a transition fromthe ground state to the first state will excite a stronger response asthere will be a greater number of vacancies in the first state.

In addition, since the measurement will be dependent on the response totwo characteristic frequencies, this may provide better discriminationof similar species; the probability of a species other than the desiredspecies absorbing the preparation pulse and responding to themeasurement pulse(s) is lower than that of it responding to themeasurement pulse alone.

Adjusting Bandwidth

As is well known, the bandwidth of a signal is inversely proportional toits duration; a long pulse (or “selective” pulse) has a better definedfrequency than a short pulse. Within limits, the field strength can beadjusted so that a pulse length appropriate to the desired bandwidth maybe used. For example, if it is desired to use an exciting pulse having aprecisely defined frequency, a long pulse and a low field strength maybe employed to produce a particular flip angle. To excite a broaderrange of frequencies, a short high intensity pulse would be used; thismay be useful in exciting samples having a spread of resonantfrequencies.

Off-resonance Experiments

An effect of moving to off-resonant conditions is that the magnitude ofthe response signal can vary according to the frequency offset. This mayneed to be compensated for by careful manipulation of the receivedsignal, or by the use of excitation at a plurality of discretefrequencies, as taught in International Patent Publication No. WO92/17794.

Another effect of moving to off-resonant conditions is that the responsesignal intensity can depend upon whether the frequency offset ispositive or negative, more intense signals sometimes being found with,say, a positive frequency offset. This effect may need to be compensatedfor by skewing the excitation frequency or frequencies to frequenciessomewhat lower than the central frequency of the frequency range ofinterest.

A pair of pulses of the same carrier frequency but different phase canproduce an effective frequency shift from the carrier frequency (thiscan be understood by considering the fourier transform of the waveform),the direction of the frequency shift being dependent on the phasechange. Thus, for example, a +90 degree shift may result in a positivefrequency shift, whereas a −90 degree (+270) shift may result in anegative frequency shift. The response signals will therefore differdepending on the direction of the phase shift, and this may be used toprovide further characterisation of the sample. Conversely, a responsesimilar to that excitable by two pulses of equal frequency but differentphase may be excited by using two pulses of different frequency; thisprovides a further method of exciting a desired response signal.

Since the phase of the received signal will change at off-resonanceconditions, this may be employed to improve determination of the exactresonant frequency. FIG. 15 shows how the real and imaginary components(solid lines) vary as a function of pulse length in response to a singler.f. excitation pulse (of strength equivalent to 40 kHz) at 4 kHz offresonance (10% of pulse strength), the dashed curve showing how themagnitude of the signal on resonance is expected to vary. The magnitudeof the signal off resonance will exceed that of the on-resonance signalfor most pulse lengths. The off resonance behaviour clearly exhibitsindependent variation in the real and imaginary components as the pulselength is varied, which can be observed as a corresponding variation inphase.

By suitable choice of off-resonance excitation, the response signal maybe selected to have a particular phase, and this may provide a furthermethod of exciting the sample. This may be useful for distinguishinggenuine NQR responses from spurious signals. A gradient, such as atemperature gradient, which affects the resonance frequency will affectthe extent to which the excitation is off resonance, and hence the phaseof the signal; this may be used to provide further characterisation ofthe sample.

Triangulation

In another arrangement (not illustrated), at least two, and preferablythree or more coils are located around the sample. Unlike the abovedescribed embodiment of FIG. 1B, the coils are not necessarilyorthogonal, but generally disposed so that the axes of any two coilssubtend an angle, preferably within a range of about 30-150 degrees inthe vicinity of the sample.

In a preferred version of this arrangement, two or more (mostadvantageously three) receiver coils are used to detect the signalproduced in response to a spatially varying field produced by a(separate) transmitter coil arrangement. The phase of the signalreceived by each coil resulting from an NQR response from a givencluster of nuclei would be expected to be substantially the same foreach receiver coil (phase changes due to different propagation distanceswould be negligible, unless the distances are large or the frequencyvery high). However, the amplitude would be expected to vary as afunction of distance (typically according to an inverse cube law) fromthe cluster to each coil. Thus, by comparing the amplitudes of signalsof like phase detected by each receiver coil, an indication of therelative distances from the receiver coils may be obtained. The phaseitself may be used to give an indication of the distance from thetransmitter coil as described above. By triangulation (that is bysolving for the position of the nuclei based on the distances from eachreference point), positional information, such as the position in spaceof the cluster may be determined.

This determination of position may be compared to or otherwise combinedwith an estimate of position determined by other methods, such as basedon the phase of the signal as discussed above. In particular, the phaseinformation may give an indication of distance from the transmitter coilas discussed above. Thus, with two receiver coils, and one transmittercoil arrangement, three distances may be determined, which may be usedto determine the position of a cluster of responsive nuclei uniquely. Ifmore coils are used, an indication of the accuracy of the measurementmay be made. It will be apparent that this information may be used inproduction of an image of the sample.

It will be understood that whilst the above method is particularlypreferable, an indication of distance may be obtained simply bymeasuring the received signal amplitude in response to a single pulse,and thus the position of responsive nuclei may be determined withoutusing the phase information which the first aspect of the inventionmakes available.

It will be understood that the present invention has been describedabove purely by way of example, and modifications of detail can be madewithin the scope of the invention.

Each feature disclosed in the description, and (where appropriate) theclaims and drawings may be provided independently or in any appropriatecombination. The abstract is incorporated herein by reference.

What is claimed is:
 1. A method of nuclear quadrupole resonance testinga sample containing quadrupolar nuclei, said method comprising: applyingexcitation to said sample, said excitation being arranged to produce aresponse signal containing detectable, substantially independentlyvarying phase and amplitude dependent components resulting from nuclearquadrupole resonance interaction between said excitation and saidquadrupolar nuclei, detecting said response signal, resolving saidresponse signal into phase and amplitude dependent components, andprocessing said response signal on the basis that both of saidcomponents vary substantially independently.
 2. A method according toclaim 1, wherein a plurality of values of said response signal aresampled, said response signal having a phase and an amplitude, and aplurality of values of a phase parameter varying as a function of saidphase of said response signal substantially independently of saidresponse signal amplitude are determined.
 3. A method according to claim1, wherein said excitation comprises first and second pulses differingin phase by a predetermined angle.
 4. A method according to claim 3,wherein said predetermined angle is about 90 degrees.
 5. A methodaccording to claim 3, wherein said pulses are substantially contiguous.6. A method according to claim 3, wherein said pulses are ofsubstantially equal duration.
 7. A method according to claim 3, whereinsaid excitation includes a third pulse arranged to produce an echo fromsaid response to said first and second pulses.
 8. A method according toclaim 1, wherein said phase and amplitude dependent components comprisetwo components having a quadrature phase relationship to each other. 9.A method according to claim 8, wherein a parameter varying as a functionof phase is obtained from a ratio of said two components.
 10. A methodaccording to claim 1, wherein said excitation has a field strength,wherein said field strength varies throughout at least a portion of saidsample according to a given pattern.
 11. A method according to claim 10,wherein said excitation has an excitation pulse duration, wherein saidfield strength and said excitation pulse duration are selected toproduce flip angles within a range of 0 to 360 degrees throughout aregion of interest of said sample.
 12. A method according to claim 1,wherein a positional parameter of said nuclei is obtained based on atleast said phase of said response signal.
 13. A method according toclaim 12 comprising applying said excitation repeatedly to said sample,and repeating said analysing to obtain a plurality of sets of saidprofile information.
 14. A method according to claim 13, wherein atleast one further set of profile information of at least one of higherresolution and signal-to-noise ratio is obtained from said plurality ofsets, and wherein at least one factor affecting said NQR response isvaried as said excitation is repeated, said at least one factorcomprising at least one of excitation pulse duration and excitationfield strength.
 15. A method according to claim 13, wherein at least onefurther set of profile information of at least one of higher resolutionand signal-to-noise ratio is obtained from said plurality of sets, andwherein at least one factor affecting said NQR response is varied assaid excitation is repeated, said excitation comprising first and secondpulses, the relative duration of said pulse varying but total durationof said pulses remaining substantially constant as said excitation isrepeated.
 16. A method according to claim 14, comprising obtaining aplurality of sets of profile information, corresponding to profiles atdifferent positions or in different directions.
 17. A method accordingto claim 12, wherein said positional parameter is a measure of positionof said nuclei in a predetermined reference frame.
 18. A methodaccording to claim 1, wherein quantity information representative of anamount of said nuclei is obtained based on at least said amplitude ofsaid response signal.
 19. A method according to claim 1 includinganalysing said components to obtain profile information representativeof a distribution of said nuclei in said sample.
 20. A method accordingto claim 19, wherein excitation is applied from two or more directionsand said profile information is obtained for each direction.
 21. Amethod according to claim 19 for forming an image of said sample,further comprising constructing an image of said sample from said atleast one set of profile information.
 22. A method according to claim 1,wherein distances of a cluster of said quadrupolar nuclei from at leasttwo reference points are determined, and wherein positional informationof said cluster is calculated based on respective ones of saiddistances.
 23. A method according to claim 1 including analysing saidcomponents to obtain profile information representative of variation ofan environmental parameter which affects said NQR response in saidsample.
 24. A method of forming an image of a sample containingquadrupolar nuclei, said method comprising: applying excitation to saidsample, said excitation having a field strength varying according to agiven function of position and being arranged to produce a detectableresponse signal resulting from NQR interaction between said excitationand said quadrupolar nuclei, said response signal being resolvable intophase-dependent and amplitude-dependent components, resolving saidresponse signal into two received components representative of saidphase-dependent and amplitude-dependent components, and based onsubstantially independent variation of both received components,producing an image representative of at least one of distribution andenvironment of said nuclei in said sample.
 25. A method according toclaim 24, wherein said excitation is repeated a plurality of times andat least one of excitation pulse amplitude and excitation pulse durationis varied as said excitation is repeated.
 26. A method according toclaim 24, further comprising producing a visual output of said image.27. A method according to claim 24, wherein forming an image includesobtaining a measure of correlation between predicted results based on amodel of said sample to data obtained from said sample.
 28. A methodaccording to claim 27, including predicting results for a series ofmodel configurations and selecting a model configuration producing bestcorrelation to data obtained from said sample as representative of saidsample.
 29. A method according to claim 24, wherein forming an imageincludes obtaining a series of time domain data for different excitationpulse lengths, fourier transforming said data to produce frequencydomain data, and fourier transforming said frequency domain data withrespect to a function of pulse length to produce profile data varyingwith a function of distance.
 30. A method according to claim 29, furthercomprising processing said profile data to produce profile data varyingwith distance.
 31. A method according to claim 24, further comprisingadjusting a scale factor based on results of a calibration experimentwith a sample of known properties.
 32. A method of probing a sample todetect quadrupolar nuclei therein, said method comprising applyingexcitation to said sample, said excitation being arranged to produce aresponse signal having detectable phase and amplitude componentsresulting from NQR interactions with said quadrupolar nuclei, detectingsaid response signal and resolving detected signal into resolvedphase-dependent and amplitude-dependent components, obtaining a phaseparameter from said resolved components, and processing both resolvedcomponents using said phase parameter to produce an output having asignal-to-noise ratio greater than that of said response signalamplitude.
 33. A method according to claim 32, wherein said processingincludes applying a first excitation to produce a first received signalin which a desired signal has a first phase dependence, and applying asecond excitation to produce a second received signal in which saiddesired signal has a second phase dependence, and detecting said desiredsignal on the basis of said first and second received signals andcorresponding measured phase dependence thereof.
 34. Apparatus fordetecting an NQR response in a sample containing quadrupolar nuclei, theapparatus comprising: excitation means arranged to generate anexcitation signal capable of exciting an NQR response having detectablephase and amplitude components; transmission means arranged to transmitsaid excitation signal to said sample; detection means arranged todetect a response signal generated by said sample to produce a detectedsignal; resolving means arranged to resolve said detected signal intofirst and second components; and signal processing means coupled to saidresolving means to receive both said first and second components andarranged to process said response signal based on substantiallyindependent variation of both phase-dependent and amplitude-dependentcomponents thereof.
 35. Apparatus according to claim 34, wherein theexcitation means is arranged to generate at least two pulses differingin phase by a predetermined angle.
 36. Apparatus according to claim 34,wherein said transmission means is arranged to generate a field having afield strength varying according to a given pattern throughout at leasta portion of said sample.
 37. Apparatus according to claim 36, furthercomprising control means arranged to cause said transmission means togenerate a plurality of said given patterns.
 38. Apparatus according toclaim 36, wherein said transmission means comprises at least first andsecond coils for producing respectively, on excitation with anelectrical signal, at least first and second fields varying in strengthas different functions of position in a vicinity of said sample, whereinadjustment of relative amplitudes of electrical signal supplied to eachcoil alters said pattern of net field.
 39. Apparatus according to claim38, wherein said transmission means includes a coil for generating afield having a substantially constant field strength in said vicinity ofsaid sample.
 40. Apparatus according to claim 34, having means to storeor to calculate the or each given pattern to provide an estimate oftransmitted field strength at a plurality of positions, and havingweighting means for determining an adjusted value of received signalstrength based on said received signal strength and said estimated fieldstrength at a position in said sample corresponding to a source of saidreceived signal.
 41. Apparatus according to claim 34, wherein saidresolving means is arranged to resolve said received signal intocomponents having a quadrature relationship.
 42. Apparatus according toclaim 34, wherein said signal-processing means includes or is coupled toprocessing means arranged to process said components to obtain datarepresentative of at least one of distribution and environment of saidnuclei in said sample.
 43. Apparatus according to claim 42, wherein saidprocessing means is arranged to construct an image of the sample. 44.Apparatus according to claim 43, wherein said processing means includesmeans for producing a visual output of said image.
 45. Apparatusaccording to claim 44, further comprising means for causing a variationin at least one environmental parameter which affects said NQR responsethroughout at least a portion of said sample.
 46. Apparatus according toclaim 34, wherein said signal processing means is arranged to samplesaid detected signal for a predetermined time, and to store twocomponents which together contain both phase and amplitude information.